There are ten problems in total. Several questions are from your text book "Microeconomics" by Bernhiem and Whinston.

Questions

1. Suppose that the demand function for corn is: Q^d = 20 - 4 P_corn + 8 P_potatos - 0.50 P_butter. Potatoes cost $0.25 per pound and butter costs $2 per pound. At what price will consumers demand 8 billion bushels per year? How does your answer change if the price of butter rises to $4 per pound?

2. Suppose the demand function for corn is Q^d = 20 - 2 Pcorn and the supply function is Q^s = 1.6 Pcorn - 7. What is the equilibrium price of corn? What is the amount of corn bought and sold?

3. Consider a linear demand function for oranges given as Q^d = 431.6 - 80.7 P. At what price will the total expenditure on oranges be largest? (Hint: total expenditure is maximized where price elasticity is -1.)

4. Suppose the demand function for corn is Q^d = 15 - 2 Pcorn and the supply function is Q^s = 5 Pcorn - 6 (same as in the worked out problem 2.2). Suppose the government needs to buy 3.5 billion bushels of corn for a third-world famine relief program. What effect will the purchase have on the equilibrium price of corn? How will it change the amount of corn that consumers buy?

(Hint: The Government's action will shift the demand curve to the right by 3.5. That is, at every price point the new demand is Q^dNEW = Q^d + 3.5. The first step is to find out the formula for the shifted demand curve.)

5. If the U.S. government were to ban imports of Canadian beef for reasons unrelated to health concerns, what would be the effect on the price of beef in the United States? How would the typical American's diet change? What if the ban suggested to consumers that there might be health risks associated with beef? (Hint: Again, think about which curve(s) will shift and what would be the effect on price and quantities.)

6. Suppose that the U.S. demand for maple syrup in thousands of gallons per year, is Q^d = 6000 - 30 P. What is the elasticity of demand at a price of $75 per gallon? (Hint: find the relevant quantity at the price of $75 using the demand function.)

7. The figure below depicts the estimated demand curve for gasoline in Detroit and Boston. When the price of gasoline is $2/gallon, the total gasoline demand is the same in the two cities (i.e., 1.5 million gallons). Can you say which demand curve is more elastic at price $2.00 per gallon?

Without knowing the mathematical formula for these two demand curves, can you say which demand curve is more elastic at price $3.00 per gallon?

8. Suppose the annual demand function for the Honda Accord is Q^d = 430 - 10 P_A + 10 P_C - 10 P_G where P_A and P_C are the prices of the Accord and the Toyota Camry respectively (in thousands), and PG is the price of gasoline (per gallon). What is the elasticity of demand of the Accord with respect to the price of Camry when both cars sell for $20,000 and fuel costs $3 per gallon? What is the elasticity with respect to the price of gasoline?

9. "If the cost of repairing your car goes up, you should do less of it." Is this statement correct? If you think the answer is yes, explain why. If you think the answer is no, give an example in which the best choice is higher when costs are higher.

10. Suppose you can hire a mechanic for up to six hours. The total benefit and the total cost functions are B(H) = 654H - 40 H2 and C(H) = 110H + 120 H². The corresponding formula for marginal benefit and marginal cost are MB(H) = 654 - 80 H and MC(H) = 110 + 240H. What is your best choice?