Please check my work, and solve problem 3

Problem 1. In less than 25 words, explain the meaning behind the concept of: Marginal cost function measures the change in cost of production when producing an 1. marginal cost function. additional unit Average cost function represents the cost of producing each unit of output, dividing total costs 2. average cost function. by the number of units produced Marginal productivity of labor measures the change in output of adding an 3. marginal productivity of labor. additional unit of labor while holding capital constant 4. isocost line. Isocost line is a curve which shows various combinations of inputs like K and L that cost the same total amount. 5. marginal rate of substitution between goods 1 and 2. MRS is the represents the amount of one good a consumer is willing to give up to consume another 6. indifference curve. good while maintaining the same level of utility. Indifference curve connects a set of consumption baskets that yield the same level of satisfaction to the Problem 2. consumer. 1. Evaluate the returns to scale of the following production function. f ( K , L) = K2 + 12 f ( 2 K, Z L ) = ZK2 + 212 . Doubled inputs =2 ( K + [? ) . constant returns to Problem 3. = 2( Q) Scale 1. Write down the maximization problem for a monopolist with cost function TC(q) = 2 + 10 when they face a demand function D(p) = 160 - 2p. 2. Find the quantity that solves the problem, and the price that the monopolist charges. Problem 4. Consider a consumer with utility function u(x, y) = x + 3y, where x and y stand for the quantities of goods 1 and 2 respectively. Mux = 1 1. Write down the marginal utility for goods 1 and 2. Muy = 3 2. Write down the MRS between goods 1 and 2. MRS =