Question

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Demand, Supply, and Market Equilibrium   

Q1. The general demand function for good A is

Q_d = 754 + 2P_A - 0.05M + 6 P_B + 10 T + 3 P_E + 2N

where Q_d = quantity demanded of good A each month, P_A = price of good A, M = average household income, P_B = price of related good B, T = a consumer taste index ranging in value from 0 to 10 (the highest rating), P_E = price consumers expect to pay next month for good A, and N = number of buyers in the market for good A.

a. Interpret the intercept parameter in the general demand function. (1 point)

b. What is the value of the slope parameter for the price of good A? Does it have the correct algebraic sign? Why? (1 point)

c. Interpret the slope parameter for income. Is good A normal or inferior? Explain. (1 point)

d. Are goods A and B substitutes or complements? Explain. Interpret the slope parameter for the price of good B. (1 point)

e. Are the algebraic signs on the slope parameters for , P_E, and N correct? Explain. (1 point)

f. Calculate the quantity demanded of good A when P_A = $2, M = $60,000, P_B =$24, = 7, P_E = $12, and N = 12,000. (2.5 point)

Q2. Consider the general supply function:

Q_s = 1,000 + 20 P - 9 P_I +25 F

where Q_s= quantity supplied, P = price of the commodity, P_I = price of a key input in the production process, and F = number of firms producing the commodity.

a. Interpret the slope parameters on P, P_I, and F. (1 point)

b. Derive the equation for the supply function when P_I= $480 and F = 60. (1 point)

c. Sketch a graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve. (1point)

d. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $1,000 and $1,500.(1 point)

e. Derive the inverse of the supply function in part b. Using the inverse supply function, calculate the supply price for 40,000 units of the commodity. Give an interpretation of this supply price. (1 point)

f. Suppose the supply curve for good X passes through the point P = $35, Qs = 2,500. Give two interpretations of this point on the supply curve. (2.5 point)

Answer 1

(Q1)

Q_d = 754 + 2P_A - 0.05M + 6 P_B + 10 T + 3 P_E + 2N

(a) The intercept being 754, it signifies that if a price of zero is charged for good A, and all other parameters are set to zero, 754 units of good A will be demanded.

(b) Slope parameter for price of good A (PA) is +2. If good A follows the law of demand, price and quantity demanded are inversely related and therefore, coefficient of PA should be negative. A positive coefficient will exist only if good A is a Giffen good (violating the law of demand).

(c) Slope parameter for price of good A (PA) is -0.05. A negative slope parameter indicates an inferior good, whose demand rises (falls) with fall (rise) in income.

(d) Slope parameter for price of good B (PB) is +6. A positive slope parameter indicates a substitute good, so a rise (fall) in price of good B increases (decreases) the demand for good A.

NOTE: As per Answering Policy, 1st 4 parts of 1st question are answered.