Answer to Question #151853 in Microeconomics for mysara griesh

Question

1. The general demand function for good A is
Qd= 600-4PA-0.03M-12PB+15T+6PE +1.5N
where Qd = quantity demanded of good A each month, PA = price of good A, M = average household income, PB= price of related good B, T = a consumer taste index ranging in value from 0 to 10 (the highest rating), PE = 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.
b. What is the value of the slope parameter for the price of good A? Does it have the correct algebraic sign? Why?
c. Interpret the slope parameter for income. Is good A normal or inferior? Explain.
d. Are goods A and B substitutes or complements? Explain. Interpret the slope parameter for the price of good B.
e. Are the algebraic signs on the slope parameters for T, PE, and N correct? Explain.
f. Calculate the quantity demanded of good A when PA = $5, M = $25,000, PB = $40,T = 6.5, PE = $5.25, and N = 2,000.

Answer 1

a. Interpret the intercept parameter in the general demand function.

ANSWER

 The  intercept parameter in the general demand function is a value of Qd when all factors are equal to zero.

The intercept parameter in some demand equation (such as Qd = f(X1, X2,…., Xn), where X1,… Xn are demand function factors) can be calculated as follows

The intercept parameter = f (0,0,…0).

The demand function can be written as follows

Qd = f(PA, M, PB,T,PE,N) = 600 – 4PA – 0,03M – 12PB + 15T + 6PE + 1,5N

Hence, its intercept parameter = 600 – 4 x 0 – 0,03 x 0 – 12 x 0 + 15 x 0 + 6 x 0 + 1,5 x 0 = 600.

This value can be interpreted as follows:

This value reflects the possible demand in the case of the goods titled A and B are free for customers and household’s income is equal to zero, and good titled A has the lowest rating, and customers know that the future price is expected to be zero. Particularly, if the good A is free the customers buy the 600 units of A.

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

ANSWER

The value of the slope parameter for the price of good A can be calculated as the first order derivative of Qd with respect to PA (dQd/dPA).

Hence, the slope parameter =  dQd/dPA = d (-4PA) / dPA = -4. It means that the increase in PA by one USD, for example, is the reason for the decrease in the Qd by 4 units.  In accordance with the law of demand, conditional on all else being equal, as the price of a good goes up, quantity demanded will go down. Hence, the non-positive slope parameter is algebraically correct.

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

ANSWER

The slope parameter for income is equal to the first order derivative of Qd with respect to M (dQd/dM). Hence, the slope parameter = dQd/dM  = d(-0,03M)/dM = - 0,03. Conclusion: if the household’s income increases, then the quantity demanded decreases. Hence the income elasticity of demand for good A is negative. Hence, A is inferior good.

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

ANSWER

The slope parameter for PB is equal to the first order derivative of Qd with respect to PB (dQd/dPB).

Hence, the slope parameter = dQd/dPB = d(-12PB)/dPB = -12.

The negative first order of Od with respect to PB means that the Cross Elasticity of Demand for A and B is negative too. Hence, the goods titled  A and B are Complements.

e. Are the algebraic signs on the slope parameters for T, PE, and N correct? Explain.

ANSWER

The algebraic sign on the slope parameter for T is equal to 15 and positive. This algebraic sign is correct because it means that any increase in the consumer taste index consistent with growth in the demand for good titled A. The customers want to buy the high-quality goods rather than the low-quality goods.

The algebraic sign on the slope parameter for PE is equal to 6 and positive. This algebraic sign is correct because it means that any increase in the expected future price consistent with growth in the demand for good titled A (the customers usually want to have stocks of this good if the price is expected to be increased in the future).

The algebraic sign on the slope parameter for n is equal to 1,5 and positive. This algebraic sign is correct because it means that any increase in the number of buyers in the market for good A consistent with growth in the demand for good titled A. The growth in the amount of customers means the positive shift in the demand function diagram.

f. Calculate the quantity demanded of good A when PA = $5, M = $25,000, PB = $40,T = 6.5, PE = $5.25, and N = 2,000.

ANSWER

Qd = f(PA, M, PB,T,PE,N) = 600 – 4PA – 0,03M – 12PB + 15T + 6PE + 1,5N

Using the equation for Qd and information regarding PA, M, PB, T, PE and N we can compute the quantity demanded of good A:

Qd = f($5, $25,000, $40, 6.5, $5.25, 2,000) = 600 – 4 x 5 – 0.03 x 25,000 – 12 x 40 + 15 x 6.5 + 6 x 5.25 + 1.5 x 2,000 = 600 - 20 - 750 - 480 + 97.5 + 3,000 = 2, 447.5

If one unit of good titled A can be divided to 2 parts, the answer is 2, 447.5.

If one unit of good titled A can not be divided to 2 parts, the answer is 2, 448.