2. Let\'s revisit the demand curve now that we know people make their decisions

Question

2. Let's revisit the demand curve now that we know people make their decisions based on the principle of rational choice (MU/P) a. Explain how an increase in income affects a consumer's MU/P calculation. How does that tie to the change in the demand curve? b. Explain how an increase in the price of a complimentary good affects a consumers MU/P calculation. How does that tie to the change in the demand curve? c. Explain how an increase in the price of a substitute good affects a consumers MU/P calculation. How does that tie to the change in the demand curve? d. An elastic demand curve is highly responsive to price. What does this say about the value of MU/P for the good? e. An inelastic demand curve in not responsive to price. What does this say about the value of MU/P for the good?

Explanation / Answer

Let us take the budget function to be I = P1X1 + P2X2

I = consumer's I come. P1 and P2 = the price of good X1 and X2 respectively.

And the utility function to be U(X1, X2)

A rational consumer aims to maximize his utility. In order to find a rational consumer's demand for a good, we maximize his utility function subject to his budget constraint.

And we thus get the equations-

MU1 = P1, MU2 = P2 and I = P1X1 + P2X2.

(a) if there is an increase in a consumer's income, his budget line will shift outwards as he will now have more to spend on each commodity. MU/P calculated, will not change however when substituted in the third equation mentioned above, will give a higher value of X1 and X2. Thus, the consumer might increase the demand for both the goods or any one good (in case of perfect substitutes) and the demand curve for the commodity will shift to the right.

(b) Now let X1 and X2 he complimentary goods. Thus, when the price of X2 rises, the demand of X2 as well as X1 will fall and vice versa (as both the goods are consumed together). If P2 rises, MU2/P2 will fall and it will not effect the MU1/P1. Since I is constant, the consumer will have to spent the same amount of money to consume higher worth of goods. So the demand of X2 and X1 will fall and there will be a leftward shift in the demand curve of good X1 (i.e. a decrease in demand) and a decrease in the quantity demanded of good X2.

(c) now let X1 and X2 be substitute goods (eg. Tea and coffee). If P2 rises, the demand for X2 will fall and the demand for X1 will rise. A rise in P2 will bring down MU2/P2. Now if, MU2/P2 is less than MU1/P1, the consumer will shift his consumption from X2 to X1 and if otherwise, he will still consume good X2 but a reduced quantity. Thus the quantity demended of X2 will fall and demand for X1 will rise.

(d) Let us now assume that X1 has a high price elasticity of demand, so if the price of X1 will rise, the quantity demanded of X1 will fall with a greater proportion and vice-versa. MU/P will fall and if MU is less than the price, the consumer will not buy the product.

(e) if the demand curve is inelastic, a change in price will not effect the quality demanded. This means that the MU/P will not change and the consumer will continue to consume the same unit of the good at an increased/ decreased price.

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