1. The following figure shows a set of representative indifference curves for Alice over apples and oranges. Alice' preferences meet all the assumption of "typical" preferences.
a. Suppose the price of an orange (PX) is $6 and the price of an apple (PY) is $2. If Alice' income is $48, graph her budget constraint and label it BC0.
b. An equation for Alice' budget constraint is:
c. Label Alice' optimal consumption point A. Under these conditions Alice will consume ______ oranges and ______ apples.
At point A, her marginal rate of substitution (MRS) will be ________ because (briefly explain how you know and what her MRS means):
2. Suppose that BEFORE THE TAX, the inverse demand for laptops is P=1200-Q while the inverse supply is P = Q.
a. WITHOUT the tax:
i. Graph the supply (S0) and demand (D0).
ii. Algebraically or graphically, find the equilibrium price and quantity of laptops.
P*= ______ Q*= ________
iii. When the market is in equilibrium, what is the consumer surplus and producer surplus? Calculate it numerically.
iv. When the market is in equilibrium, what is the price elasticity of demand at (Q*, P*)? Calculate it numerically and interpret your calculation.
b. Now, suppose the government imposes a $400 per unit tax on suppliers of laptops. WITH the tax:
i. Write an equation for the new inverse supply (Stax).
ii. Algebraically or graphically, find the equilibrium price and quantity of laptops with the tax.
P'=______ Q'= _______
iii. When the market is in equilibrium with the tax, what is the government revenue? Calculate it numerically.
iv. Is there any deadweight loss from this per unit tax? If so, calculate it numerically and label it on the graph.
c. A local politician thinks the tax might be more popular if the $400 per unit tax were evenly divided between consumers and producers. That is, consumers would be statutorily responsible for a $200 tax and producers would be statutorily responsible for a $200 tax. Theoretically, how would this affect economic incidence?
3. Andrew spends all his income on DVDs and other things, Y. The following graph represents a set of his convex indifference curves (I) representing his preferences for DVDs and other things.
a. Andrew has an income of $360 to spend on DVDs and Y. If the price of DVDs, PD, is $20 and the price of Y, PY, is $2, draw Andrew's budget constraint (BC0) and label his optimal consumption point A.
b. If the price of DVDs, PD, increases to $60 and everything else stays the same, draw Andrew's new budget constraint (BC1) and label his new optimal consumption point C. If necessary, draw new indifference curves.
At point C, Andrew consumes ____ DVDs and ____Y.
c. On the graph, draw (as carefully as possible) Andrew's budget line (BC2) that reflects the substitution effect. Label this intermediate consumption point B. With the substitution effect ONLY: At point B, Andrew consumes ______DVDs and _____Y.
d. Does the substitution effect of the increase in the price of DVD make him buy more or less DVDs? How many more or less?
e. Can you tell whether DVDs are a normal or inferior good? Why or why not?