Need solutions.

The managing director, Mr Erasmus, has asked for assistance to determine whether the marketing manager's proposal is a viable option in helping to boost the company's revenue. In the current financial year 40 000 jerseys were sold, which was 60 000 jerseys less than what was sold previously.

The marketing team, through their research, has indicated that if the selling price was reduced by 25%, then unit sales would increase by 60% for the next financial year.

Together with the marketing department's research, the financial manager has provided with the following forecasted information for the year ending 31 March 2022.

Through negotiation with suppliers and the improved exchange rate, the costs to manufacture each jersey are expected to decrease by 10%.

Other operating income is expected to increase by 5%.

Operating expenses are expected to increase by 12%.

Due to the decline in interest rates, interest income is expected to be three quarters of the

amount earned for the year ending 31 March 2021 whilst the interest expense is expected to decline by R 50 000.

Mr Erasmus has indicated that the proposal will only be implemented if the forecasted net profit before tax percentage exceeds the industry average of 15%.

REQUIRED:

Prepare the budgeted statement of comprehensive income using the information above to determine whether the marketing manager's proposal should be implemented.

Considering the current rise in the inflation rate the company is concerned that the risks associated with this purchase maybe higher than previously thought.complete Therefore, they are raising the discount rate 13% for evaluating proposals of this type.

a. Should the company purchase the new equipment? Support your decision with facts.

b. If they do decide to go ahead with this project what is the most they can pay for the

machinery

Consider the Mortensen-Pissarides model in continuous time. Labor force is normalized to 1. Un- employed workers, with measure u 1, and rms with one vacancy each and total measure v search for each other, and v is determined endogenously by free entry. A CRS matching function, m(u; v), brings together unemployed workers and vacant rms; m is increasing in both arguments. As is standard, let v=u denote the market tightness and q() = m=v the arrival rate of unemployed workers to the typical rm. What is dierent here compared to the baseline model is that a match" and a productive job" are not equivalent by default. When a worker and a vacant rm meet, the rm must train the worker before she can start producing. A formed match turns into a productive job at a stochastic rate, a 2 (0;+1), so that 1=a can be thought of as the average time necessary for the training to be completed. Assume that the rm and the worker determine the wage level when they rst meet (i.e., even before training starts), through Nash bargaining, with 2 (0; 1) representing the workers power. However, the wage upon which they have agreed will only be paid to the worker when she starts producing.1 To close the model, we will make a few more standard assumptions. The output of a productive job is p > 0 per unit of time, and while a rm is searching for a worker it has to pay a search (or recruiting) cost, pc > 0, per unit of time. Firms that are training their workers do not pay this cost (they are done recruiting). Productive jobs are exogenously destroyed at rate > 0 (only productive jobs are subject to this shock; matches at the training stage cannot be terminated). All agents discount future at the rate r > 0, and unemployed workers enjoy a z > 0 per unit of time. While at the training stage the worker does not receive an unemployment benet (a trainee is not unemployed).2 (a) Dene the value functions of the typical rm at one of the three possible states: V (with an open vacancy), M (matched but still at the stage of training), and J (matched at the stage of production). Describe the steady state expressions for these value functions. (b) Dene the value functions of the typical worker at one of the three possible states: U (unemployed), T (matched but still at the stage of training), and W (matched at the stage of production). well Describe the steady state expressions for these value functions. (c) Combine the free entry condition (i.e., V = 0) with the expressions that you provided for V;M; J in order to derive the job creation curve of the economy. (d) Using the same methodology as in the lecture (adjusted only to accommodate the dierences in the new environment), derive the wage curve for this economy. (e) Provide a restriction on parameter values such that a steady state equilibrium pair (w; ) exists. Is it unique? (no need for a lengthy discussion) (f) What is the eect of a decrease in a on the equilibrium w and ? Explain intuitively (but shortly). (g) Describe the Beveridge curve of this economy by looking at the ows of workers in and out of the various states. What eect will the decrease in a (discussed in the previous part) have on unemployment?

Consider the standard growth model in discrete time. There is a large number of identical households normalized to 1. Each household wants to maximize life-time discounted utility U(fctg1t=0) = 1X t=0 tu(ct); 2 (0; 1): Each household has an initial capital k0 at time 0, and one unit of productive time in each period that can be devoted to work. Final output is produced using capital and labor, according to a CRS production function F. This technology is owned by rms (whose measure does not really matter because of the CRS assumption). Output can be consumed (ct) or invested (it). Households own the capital (so they make the investment decision), and they rent it out to rms. Let 2 (0; 1) denote the depreciation rate of capital. Households own the rms, i.e. they are claimants to the rmsprots, but these prots will be zero in equilibrium. The function u is twice continuously dierentiable and bounded, with u0(c) > 0, u00(c) < 0, u0(0) = 1, and u0(1) = 0. Regarding the production technology, we will introduce the useful function f(x) F(x; 1)+(1)x, 8x 2 R+. The function f is twice continuously dierentiable with f0(x) > 0, f00(x) < 0, f(0) = 0, f0(0) = 1, and f0(1) = 1 . In this model the government taxes householdsinvestment at the constant rate 2 [0; 1]. The govern- ment returns all the tax revenues, T, to the households in the form of lump-sum transfers. Throughout this question focus on recursive competitive equilibrium (RCE). (a) Write down the problem of the household recursively.3 Carefully distinguish between aggregate and individual state variables. Then, dene a RCE. Hint: Writing down the budget constraint correctly is essential for this question, so think carefully: the household can choose to allocate its wealth between consumption and investment in any way it likes, but for any unit of resources allocated into investment, a fraction of that amount will be subtracted from the households budget (and it will be returned to them in the form of a lump-sum transfer). (b) Write down the dynamic equation that the aggregate capital stock follows in this economy. Hint: Obtain the Euler equation for the typical household and impose the RCE conditions. (c) Now focus on steady-states. Describe the steady-state equilibrium value of the aggregate capital stock in this economy, and denote it by K( ). If the formula you arrived at involves the function F, I recommend that you replace it with the function f in order to answer the next parts. (d) Describe the value of K when = 0 and when = 1. (e) In class, we studied the RCE steady state level of capital in an economy where the government taxed the income from renting capital (as opposed to investment, which is the case here). In that model, we saw that for = 1 the equilibrium capital stock reached zero. Based on your answer to part (d), does this also happen here? Provide an intuitive explanation of why (or why not). (f) Let F(K;N) = KaN1a, a 2 (0; 1). Provide a closed-form solution for K( ). (g) Now focus on the special case where F(K;N) = K 1 2N 1 2 . Calculate the governments total tax revenue, T, and plot it as a function of the tax rate (the so-called Laer curve). Which value of maximizes tax revenues?

Consider the discrete time monetary-search model we saw in class. As in the baseline model, in the day time trade takes place in a decentralized market characterized by anonymity and bilateral meetings (call it the DM), and at night trade takes place in a Walrasian or centralized market (call it the CM). There are two types of agents, buyers and sellers, and the measure of both is normalized to the unit. The per period utility is u(q)+U(X)H, for buyers, and q+U(X)H, for sellers; q is consumption of the DM good, X is consumption of the CM good (the numeraire), and H is hours worked in the CM. In the CM, one hour of work delivers one unit of the numeraire. The functions u;U satisfy standard properties. What is important here is that there exists X > 0 such that U0 (X) = 1. Goods are non storable, but there exits a storable and recognizable object, called at money, that can serve as a means of payment. The supply of money, controlled by the monetary authority, follows the process Mt+1 = (1 + )Mt, and new money is introduced via lump-sum transfers to buyers in the CM. So far, this is just a description of the model we saw in class. What is dierent here is that only a fraction of buyers turn out to have a desire to consume the DM good in the current period; let us refer to these buyers as C-types (for consumption) and to the remaining 1 buyers as N-types (for no-consumption). The shock that determines each buyers type in every period is iid. A buyer learns her type after all CM trade has concluded but before the DM opens. To make things interesting we will assume that between the CM and the DM there is a third market, where C-types and N-types can meet and trade liquidity", i.e., money. Let us refer to this market as the loan market (LM).4 The LM is a bilateral market for loans, where N-types, who may carry some money that they do not need, meet C-types, who may need additional liquidity. A CRS matching function f(; 1 ) brings the two types together. Importantly, the LM is not anonymous, so that agents can make credible (and enforceable) promises. Hence, when an N-type and a C-type meet, they mutually benet from a contract specifying that the N-type will give l units of money to the C-type right away, and the C-type will repay d (for debt) units of the numeraire good in the forthcoming CM. After the LM trades have concluded (for the agents who matched with someone), C-types proceed to the DM, where they use money to purchase goods from sellers. Assume that all C-type buyers match with a seller. Notice that I have not said anything about the splitting of the various surpluses (i.e., bargaining), because this information will not be necessary for what I am asking here. Let W(:) be the CM value function of a buyer, and V (:) the DM value function of a C-type buyer (since only these buyers visit the DM). Also, let i(:) be the LM value function of a type-i buyer, i 2 fC;Ng. Your task in this question is to describe these value functions. I am not asking you to analyze them. I recommend that you draw a graph summarizing the timing of the model. (a) Describe the function W(:), and show that it is linear in all its arguments/state variables (what these arguments are, however, is for you to determine). (b) Let (q; p) be the quantity of good and the units of money exchanged in a typical DM meeting. Let (l; d) be the size of the loan (in dollars) and the promised repayment (in terms of the numeraire) specied in a typical LM meeting. What variables do the terms q; p; l; d depend on? Hint: Provide quick answers of the form q is a function of the money holdings of the (C-type) buyer". (c) Describe the function V (:), where, again, determining the state variables is your task. (d) Describe the functions i(m), i 2 fC;Ng, for a buyer who enters the LM with m units of money.

This problem analyzes the eect of future nancial constraints on current investment decisions. Consider an economy with two dates, denoted by t = 1; 2. There are two goods: consumption and capital. There is a continuum of entrepreneurs and a continuum of consumers. All individuals have linear utility and consume only in period 2, so U = E[c2]. There is a xed supply of capital k, initially owned by the consumers. Consumers are endowed with a large amount of consumption good in each period and they can store this good between dates, such that if they store one unit of the consumption good in t = 1 they get one unit of the good in t = 2. The entrepreneurs have access to a linear technology that produces A units of consumption good in period 2 per unit of capital they own. The consumers have access to a concave technology G(~k), where ~k denotes the capital owned by consumers in period 2. Assume limk!0G0(k) = 1 and G0(k) = 0. The entrepreneurs enter period 1 with a given net worth N1 in terms of consumption goods. Assume agents can trade a risk-free bond b2 that pays an interest rate r. a) Argue that the gross rate of return on the risk-free bond is equal to 1 (i.e., the net return, r, is zero). b) Suppose that entrepreneurs face no borrowing constraints. State the optimization problems of an entrepreneur and a consumer. Show that the equilibrium capital price is q1 = A and the entrepreneurs buy k, where G0(k k) = A. c) Suppose that the entrepreneurs cannot borrow at all, so q1k2 N1. Find the equilibrium price and allocation, show that q1 A in equilibrium and that the expected utility of the entrepreneur is A q1 N1 (18) irrespective of whether the constraint q1k2 N1 binds or not. Show that q1 is increasing in N1 for N1 < Ak. Let's add one period prior to period 1, period 0. Now the economy has three dates t = 0; 1; 2. In t = 0 the entrepreneurs have initial net worth N0 (in consumption goods). Then they borrow b1 from the consumers and buy capital k1 at the price q0 (capital never depreciates). The technology in period 1 is the same as in period 2: consumers produce using the concave technology G(k) and entrepreneurs have a linear technology. However the productivity of the entrepreneurs at t = 1 is a random variable a distributed on [a; a] with E[a] = A. The productivity in t = 2 is xed at A