Question

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

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

        Qd = 100 – 2.5P + 0.25M - 5PY + 1PZ

Where Qdis quantity demanded of good X, P is price of good X, M is consumer income (in thousands), PY is price of good Y, and PZ is price of a related good, Z.                                                             (18 pts)

a. Based on the estimated demand function, what is the relationship between good X and good Y; between good X and good Z? Explain? Is good X a normal good or an inferior good? Explain.

b. Determine the effect of $1000 increase in consumer income on the demand for X, other things remaining the same.

c. Derive the equation of the (direct) demand function if consumer incomes are $30,000, the price of good Y is $10 and the price of good Z is $20.

d. Derive the inverse of the demand function determined in part c above. Using the derived inverse demand function, calculate the demand price for 190 units of the good. Give an interpretation of this demand price and its importance for making managerial decisions.

       The general supply function for the product X estimated to be

        Qs = –100 + 10P – 2.5PI + 0.25PR

Where Qs is quantity supplied of good X, P is price of good X, PI is the price of inputs to good X, and PR 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? Explain.

f. Derive the equation for the supply function if the input prices are $10, and the price of R is $20.

g. What is the minimum price at which the producer will supply any of the good X at all?

h. Based on your results above, determine the equilibrium price and quantity of good X.

i. What is the market outcome if price is $20? What kind of changes would you expect to take place in the market? Why?

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