Question

Maude thinks delphiniums and hollyhocks are perfect substitutes, one for one. If delphiniums currently cost $5 per unit and hollyhocks cost $6 per unit and if the price of delphiniums rises to $8 per unit,

a. the income effect of the change in demand for delphiniums will be bigger than the substitution effect.

b. there will be no change in the demand for hollyhocks.

c. the entire change in demand for delphiniums will be due to the substitution effect.

d. 1/3 of the change will be due to the income effect.

e. 2/3 of the change will be due to the income effect.

PLEASE SHOW ALL WORK

Answer 1

c. the entire change in demand for delphiniums will be due to the substitution effect.

Let delphiniums and hollyhocks be represented by D and H respectively.
Price of D, PD = $5 and price of H, PH = $6
New price of D, PD' = $8

Utility function can be written as:
U = D + H

As the goods are substitutes so demand for D and H depends on the relationship between MRS and their price ratio.

MRS_D,H = MUD/MUH =

Price ratio = PD/PH = 5/6 = 0.83

As MRS > price ratio so only delphiniums will be consumed.

New price ratio = PD'/PH = 8/6 = 1.33

Now, MRS < Price ratio, so only hollyhocks will be consumed. Thus, H is substituted for D after the price change. This means there is only substitution effect.