1 Question 1 The most amount of money a person is willing to pay for an asset is equal to the cash flow that person expects to receive from that asset. According to Baye and Prince (2022), the present value (PV) of a future value (FV) received in n years in the future is πΉπ ππ = (1+π)π Here, FV is $250,000, n is 5, and i is the opportunity cost, which is 8%. Payment will be received at the end of every year for 5 years. So, PV=PV1+PV2+PV3+PV4+PV5 = 250,000 1+0.08 250,000 250,000 250,000 250,000 + (1+0.08)2 + (1+0.08)3 + (1+0.08)4 + (1+0.08)5 = 231,481.48+214,334.71+198,458.06+183,757.46+170,145.80 = 998,177.51 Therefore, the present value of potential profits over the next five years is $998,177.51, which is the most the person is willing to pay for the asset. Question 2 1. Given the supply function Qxs = −30 + 2Px − 4Pz, we insert Px=$600 and Pz=$60 into the supply function to get the total quantity of product X produced is Qxs = -30+2600460= 930 2. If putting Px = $80 and Pz = $60, we get the quantity supplied of product X is -30+160240= -110. This is a negative value that means no supply of X. So the total amount produced is 0. 3. Given Qxs = - 30 + 2Px - 4Pz and Pz= $60, so Supply function: Qxs = - 30 + 2Px - 4(60) = -270 +2Px. Inverse supply function: Px = 135+0.5Qxs PA 1 - PROFESSIONAL ASSIGNMENT 2 Question 3 1. According to Baye and Prince (2022), the own price elasticity of demand measures the responsiveness of quantity demanded to a change in price. The own price elasticity of demand for good X: πΈππ₯,ππ₯ = πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π πππππππ‘πππ πβππππ ππ π‘βπ πππππ ππ π πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π −6% = = -5 So the percentage change in quantity demanded is 30%. Thus, the consumption of good X will increase by 30% if the price of good X decreases by 6%. 2. As Baye and Prince (2022) explained, the cross-price elasticity of demand measures the responsiveness of the demand for a good to changes in the price of a related good. The cross-price elasticity of demand between good X and Y, denoted πΈππ₯,ππ¦ , is defined as: PA 1 - PROFESSIONAL ASSIGNMENT πΈππ₯,ππ¦ = 3 πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π πππππππ‘πππ πβππππ ππ π‘βπ πππππ ππ π πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π 7% = =3 So the percentage change in the quantity demanded of X equals 21%. The consumption of good X will increase by 21% if the price of good Y increases by 7%. 3. The own advertising elasticity of demand for good X defines the percentage change in the consumption of X that results from a given percentage change in advertising spent on X (Baye & Prince, 2022, p. 90). The own advertising elasticity of demand for good X is defined as: πΈππ₯,π΄π₯ = π‘βπ πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π π‘βπ πππππππ‘πππ πβππππ ππ πππ£πππ‘ππ πππππ‘ π‘βπ πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π −2% = =4 So the percentage change in the quantity demanded of X is equal to -8%. Therefore, the consumption of good X will decrease by 8% if the advertising in X goes down by 2%. 4. Income elasticity is a measure of the responsiveness of consumer demand to changes in income (Baye & Prince, 2022, p. 88). The income elasticity of demand for good X, denoted πΈππ₯,π , is defined as: πΈππ₯,π = πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π πππππππ‘πππ πβππππ ππ ππππ π’ππ ππππππ πππππππ‘πππ πβππππ ππ π‘βπ ππ’πππ‘ππ‘π¦ ππππππππ ππ π 3% = = -1 So the percentage change in the quantity demanded of X equals -3%. As a result, the consumption of good X will decrease by 3% if the consumer income increases by 3%. PA 1 - PROFESSIONAL ASSIGNMENT 4 Question 4 1. The slope of the budget line through point A is -20/20=-1, If the price of good X is $5, the price of Y is $5. 2. According to Baye and Prince (2022), the maximum affordable quantity of good X π consumed is π = ππ₯, which represents the horizontal intercept of the budget line. In the accompanying figure, the horizontal intercept is 20. Given the price of good X is $5 and the maximum quantity consumer can spend on good X is 20, the consumer’s income is $5(20)=$100. 3. The consumer’s expenditures on good X, plus her or his expenditures on good Y, do not exceed the consumer’s income. At point A, the consumer purchases 10 units of good Y at a price of $5 each. The income spent on purchasing good Y is $50. The consumer has $50 left for the purchase of good X at a price of $5 per unit. The number of units of good X purchased equals $50/$5=10. 4. The budget line through point B represents that the maximum affordable quantity of good X consumed is 20 if the consumer spends the entire income on good X. If the consumer spends the entire income on good Y, the maximum quantity of good Y that is affordable is 40. Since the maximum affordable quantity of Y doubled, the price of the good Y decreased by 50%, while the price of good X stayed the same. The decreased price of Y might result from new technology and increased productivity. The consumer benefits from the price increase because they can buy twice as many goods Y with the same amount of money. PA 1 - PROFESSIONAL ASSIGNMENT 5 References Baye, M. R., & Prince, J. T. (2022). Managerial economics and business strategy (10th ed.). McGraw-Hill Education.
