A firm can produce xylophones (X) and yo-yos (Y) according to the following function: Y=140-0.05X², where X is the number of xylophones that it produces and Y is the number of yo-yos.

MRS=(2/3X^-1/3Y^1/3)/(1/3X^2/3Y^-2/3) MRT=-0.1X

1.Solve for Mr. Ma's optimal choice of X and Y, i.e. the number of xylophones and yo-yos that he would optimally want to produce in order to maximize his consumption utility. [Hint: you can solve for this easily by using the fact that, at the optimal point, Mr. Ma's MRS must be equal to his firm's MRT.]

Write solution for the optimal choice of X below.

2.Write solution for the optimal choice of Y below.

3.If we had a competitive production economy, where the firm and the consumer are as described above, what would the relative price of xylophones to yo-yos, i.e. p_X/p_Y, have to be in equilibrium, in order for the market to clear? (Remember that in the competitive equilibrium, MRS=MRT=p_X/p_Y.)