A firm can produce xylophones (X) and yo-yos (Y) according to the following function: Y=151-0.09X2, where X is the number of xylophones that it produces and Y is the number of yo-yos. If the firm decided to produce only yo-yos, how many yo-yos will it produce? [Use up to two decimal places in all of your answers below.] Answer: If the firm decides to produce only xylophones, how many xylophones will it produce? Answer: How many yo-yos will the firm be able to produce, if it produces 9 xylophones? Answer:How many xylophones will the firm be able to produce, if it produces 90 yo-yos? Answer: Remember that the Marginal Rate of Transformation (MRT) can be found by computing the slope of the Production Possibilities Frontier (PPF), with yo-yos (Y) on the vertical axis and xylophones (X) on the horizontal axis. What is the firm's Marginal Rate of Transformation (MRT), in absolute value, at the point where it is producing 9 xylophones? Express the value of the MRT in absolute terms, i.e. without a negative sign in front. Answer: What is the firm's Marginal Rate of Transformation (MRT), in absolute value, at the point where it is producing 90 yo- yos? Express the value of the MRT in absolute terms, i.e. without a negative sign in front. Answer:Musician Yo-Yo Ma is the owner of this company, and actually produces yo-yos and xylophones for his own consumption. His preferences over xylophones (X) and yo-yos (Y) are given by the following utility function: U=X2/3 y1/3. Compute Mr. Ma's Marginal Rate of Substitution (MRS), defined as the marginal utility of xylophones, relative to the marginal utility of yo-yos. What is the value of Mr. Ma's MRS at the point where his production of xylophones is equal to 9? (Remember that he consumes everything that he produces.) Express the value of the MRS in absolute terms, i.e. without a negative sign in front. Answer: What is the value of Mr. Ma's MRS at the point where his production of yo-yos is equal to 90? (Remember that he consumes everything that he produces.) Express the value of the MRS in absolute terms, i.e. without a negative sign in front. Answer: 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 your solution for the optimal choice of X below. Answer:Write your solution for the optimal choice of Y below. Answer: 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. px/py, have to be in equilibrium, in order for the market to clear? (Remember that in the competitive equilibrium, MRS=MRT=px/PY.)