Solve clearly...

Question 2 Assume that the function U(x, y) = x03 yo.5 is the utility function of a Peng Yao, a rich consumer of two goods in quantities x and y, respectively. The price of x is px = 5 and the price of y is py = 8 Peng Yao's income is m = 160. (a) Find the optimal consumption choice of Peng Yao. Optimal bundle for Peng Yao: (x,y)=(12,12.5) V/3 (b) Verify that at the optimum that you found the marginal rate of substitution equals the price ratio. Explain in terms of economic theory why this should be the case! MRS=3/5(y/x) At Eqm, MRS (x=12, y=12/5)=0.625=5/8=Px/Py (Proved) This should be the case because at Eqm, gc is tangent to BC, the slope of go=MRS=slope of BC-price ratio 2 (c) Assume that the price of x falls to px = 4. i. Calculate Peng Yao's demand for x and y at the new price. (x, y )new (15,12.5) 2 ii. Calculate the compensated income, m'. m'=147.165 iii. Decompose the change in demand for good x into a substitution and an income effect. Substitution: 1.795 Income effect: 1.205 XX2