Introduction to Quantitative Economics Assignment -
Section A: Answer ALL THREE questions
Q1. Mary's utility function is U(b, c) = b + 100c - c2, where b is the number of silver bells in her garden and c is the number of cockle shells. She has 500 square feet in her garden to allocate between silver bells and cockle shells. Silver bells each take up 1 square foot and cockle shells each take up 4 square feet. She gets both kinds of seeds for free.
(a) What is Mary's budget constraint? (Hint: Write down her "budget constraint" for space.)
(b) To maximize her utility, given the size of her garden, how many silver bells and cockle shells should Mary plant?
(c) If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of silver bells and cockle shells?
Q2. The Grand Theatre is a movie house in a medium-sized town. This theatre shows unusual films and treats early-arriving moviegoers to live organ music and Bugs Bunny cartoons. If the theatre is open, the owners have to pay a fixed nightly amount of $500 for films, ushers, and so on, regardless of how many people come to the movie. For simplicity, assume that if the theatre is closed, its costs are zero. The theatre has as customers, students from a nearby college as well as resident nonstudents. The nightly demand for Grand Theatre movies by students is Qs = 220-40PS, where Qs is the number of movie tickets demanded by students at price Ps. The nightly demand for nonstudent moviegoers is Qn = 140-20Pn. We assume both Qs, Qn ≥ 0.
(a) If the Grand Theatre charges a single price, PT, to everybody, then at prices between 0 and $5.50, what is the inverse demand function? What is the profit-maximizing number of tickets for the Grand Theatre to sell if it charges one price to everybody?
(b) When they come to see movies, the students make a lot of noise and disturb the town's residents. The residents of the town complain to the local government authority about this and insist that they be taxed at a higher rate. The students argue that they spend their money in town and enrich residents and hence should not be taxed. What argument is more compelling? Explain using concepts studied in class.
Q3. Albatross Airlines (AA) has a monopoly on air travel between Peoria and Dubuque. If Albatross makes one trip in each direction per day, the demand schedule for round trips is q = 160-2p, where q is the number of passengers per day. (Assume that nobody makes one-way trips) There is an "overhead" fixed cost of $2,000 per day that is necessary to fly the airplane regardless of the number of passengers. In addition, there is a marginal cost of $10 per passenger. Thus, total daily costs are $2,000+10q if the plane flies at all.
(a) Calculate the profit-maximizing price and quantity and total daily profits for Albatross Airlines.
(b) Suppose that AA stuck with one plane. If another firm with the same costs as Albatross Airlines were to enter the Dubuque-Peoria market with a plane of its own and if the industry then became a Cournot duopoly, would the new entrant make a profit?
(c) Suppose that AA stuck with one plane and another firm entered the market with a plane of its own. If the second firm has the same cost function as the first and if the two firms act as Cournot oligopolists, what will be the price, quantities, and profits?
Section B: Answer ALL THREE questions
Please use a separate booklet.
Q4. Suppose a closed economy can be described by the following Cobb-Douglas production function:
Y = KαLβT1-α-β
where Y is output, K is capital, L is labour and T is land. Suppose 0 < α, β < 1.
(a) Show that this production function has constant returns to scale.
(b) Suppose that the price of output is given by P, the rental price for capital is given by R, the wage is given by W and the rental price for land is given by V. Derive the real rental price of capital, the real wage and the real rental price for land. What is the income distribution between the three factors of production?
(c) Assume that savings S in the economy are exogenous and investment I depends negatively on the real rental price of capital (which can also be regarded as the real interest rate). Suppose an earthquake destroys some of the economy's capital stock K. How does this affect your answer to question (b) and how does the earthquake affect investment? Draw a diagram to illustrate the effect on savings and investment. Don't forget to label your diagram.
Q5. Suppose there are two countries, Albion and Gallia. They have separate currencies (crowns for Albion and francs for Gallia). In each country there are two goods whose prices enter the consumer price index with equal weights (as a simple average).
(a) Assume the prices are p1 = 10 crowns and p2 = 30 crowns, and p1* = 120 francs and p2* = 200 francs. One unit of the Albion currency is worth two units of the Gallia currency. Compute Albion's real exchange rate.
(b) What is the economic interpretation of the real exchange rate? Explain in words.
(c) Now suppose purchasing power parity (PPP) holds. Assuming that the goods prices do not change, what would be the nominal exchange rate? Provide an intuitive explanation.
Q6. Consider the Mundell-Fleming model to answer the following questions. Suppose the economy is in a long-run equilibrium, and then the government implements a fiscal expansion (G rises).
(a) Draw the IS* and LM* curves and show how these curves shift in response to the government spending shock. Do not forget to label your diagram.
(b) What would happen to equilibrium income, the nominal exchange rate and the trade balance (i.e., net exports NX) in the short run as a response to this shock if the nominal exchange rate was floating?
(c) What would happen to equilibrium income, the nominal exchange rate and the trade balance as the economy moves from the short run to the long run if the nominal exchange rate was floating?
(d) What would happen to equilibrium income, the nominal exchange rate and the trade balance in the short run as a response to the shock if the nominal exchange rate was fixed?
(e) Explain in words the economic mechanism behind the effects in (d).