Question

Stuart's utility function for goods X and Y is represented as U(X,Y)=X0.8Y0.2. Assume that his income is $100 and the prices of goods X and Y are $20 and $10, respectively.

 

(d) Derive the demand curve for good X and demand curve for good Y.

 

Now a government subsidy program lowers the price of X from $20 per unit to $10 per unit.

 

(e) Calculate and graphically show the change in good X consumption resulting from the program.

 

(f) Graphically show the change in consumption attributable to the separate income and substitution effects.

 

(g) Show (graphically) how much the program cost the government.

 

Answer 1

Solution:

d.). The demand curve for Good X:

Y = $0.25X\frac{Px}{Py}$

I = PxX + PyY

I = PxX + Py($0.25X\frac{Px}{Py}$)

I = PxX + 0.25XPx

I = 1.25XPx

X = $\frac{I}{1.25Px}$

 

The demand curve for Good Y:

X = $4Y\frac{Py}{Px}$

I = PxX + PyY

I = Px($4Y\frac{Py}{Px}$) + PyY

I = 4YPy + PyY

I = 5YPy

Y = $\frac{I}{5Py}$

e.). Budget constraint: I = PxX + PyY

100 = 20X + 10Y

New budget constraint after subsidy on Good X:

100 = 10X + 10Y

Good X = $\frac{100}{10}$ = 10

Consumption of good X will increase by 5

This is depicted by the below graph:

 

 

f.). This is depicted by the below graph:

 

g.). This is depicted by the below graph: