Please help me with these questions. Thanks a lot!!!

Problem 1:

J the consumer consumes only two goods with quantities x1 and x2 respectively. J's utility function is: u(x1; x2) = ln x1 + x2 + 2. Let the prices be p1 = 1; p2 = 6 and J's income be m = 60

(a) What are J's optimal quantities demanded of each good? Graph his budget line and label his optimal bundle as A. (Hint: You may want to derive J's optimal quantities demanded for any p1; p2; m and then just plug in the given values) Suppose now that the government puts a quantity tax that increases the price of good 1 to p'1 = 2.

(b) What are J's optimal quantities demanded of each good after the tax is imposed? Plot his new budget line on the graph from (a) and denote his optimal bundle by C.

(c) To how much must J's income be adjusted after the tax is imposed so that he can just afford his optimal bundle from (a)?

(d) What would J's optimal quantities demanded for each good be with the adjusted income as in (c) at the after-tax prices. Plot the budget line corresponding to this bundle on your graph and denote the optimal bundle by B.

(e) Given your resultsfind the income and substitution effects of the change in p1 on J's consumption of each good. Explain briefly the intuition for the results.

Problem 2 (30 pts) Explain your answers! The market demand function for computer games is qD(p) = 300-6p and the market supply function is qS(p) = 4p:

(a) Find the equations of (express price in terms of quantity) and plot the demand and supply curves corresponding to the given market demand and supply functions. Find the market equilibrium price and quantity p and q .

(b) Find the producer's surplus and consumer's surplus at the equilibrium.

(c) What is the price elasticity of demand at the equilibrium point?

(d) Derive the equation of the marginal revenue curve and compute the marginal revenue at the equilibrium point in (a).

(e) Given the demand function, at what price would total revenue be maximized?

(f) Suppose a quantity tax of $5 per game is imposed on the computer game suppliers. What is the new equilibrium price paid by the consumers? What is the new equilibrium price received by producers? How much is the tax revenue? How much is the deadweight loss of the tax? Use a graph to explain your answer