Question

Consider that the general demand function for a product X is estimated to be

              Q_d = 500 – 5P + 0.5M + 10P_Y - 2P_Z

Where Q_d is quantity demanded of good X, P is price of good X, M is consumer income (in thousands), P_Y is price of good Y, and P_Z is price of good Z.        

a. Based on the estimated demand function, what is the relationship between good X and good Y; between good X and good Z?                       (2 pts)

       X and Y are substitutes. This is known because there is a positive relationship between the price of good Y and the demand for good X. Therefore, as the price of good Y rises, consumers will buy more of good X. On the other hand, X and Z are complements. This is known because there is a negative relationship between the price of good Z and the demand for good X. Therefore, as the price of good Z rises, consumers will buy less of good X.

b. Based on the estimated demand function, is good X a normal good or an inferior good? Explain.                                                   (2 pts)

X is a normal good. This is known because there is a positive relationship between income and the quantity demanded of good X.

c. Derive the simplified (quantity demanded as a function of price) demand function if consumer incomes are $30,000, the price of good Y is $10 and the price of good Z is $20.            

       Qd= 500-5Px+0.5I+10Py-2Pz

= 500-5Px+0.5(30,000)+10(10)-2(20)

=15,560 - 5Px                                                              (2 pts)

      

The general supply function for the product X estimated to be

       Q_s = –200 + 20P – 5P_I + 0.5P_R

Where Q_s is quantity supplied of good X, P is price of good X, P_I is the price of inputs to good X, and P_R is price of related (in production) good R.

e. Based on the supply function above, what is the relationship between good X and good R?                                                            (2 pts)

f. Derive the simplified (quantity supplied as a function of price) supply function if the input prices are $10, and the price of R is $20.              (2 pts)

                           

g. Based on your results above, determine the equilibrium price and quantity of good X.                                                                  (5 pts)

h. What is the market outcome if price is $40? What do you expect to happen in the      market? Why?

Answer 1