1. After the start of the COVID-19 crisis, a lot of liquor and perfume manufacturers switched to producing hand sanitiser.  After that happened, the quantity supplied in a certain market for hand sanitiser was given by

Qs  = −12.17 + 0.1Phs − 0.03Pg  − 0.07Pp + 0.4N,

where Qs  is the quantity of hand sanitiser supplied measured in hundreds of litres, Phs  is the price of hand sanitiser per 100 litres, Pg  is the price of gin per bottle, Pp  is the price of plastic (input needed for the manufacture of hand sanitiser containers) per tonne, and N is the number of distilleries that can produce hand sanitiser.

(a)  (3 marks) Keeping in mind that gin is not an input good for the production of hand

sanitiser, how are hand sanitiser and gin related as goods? Justify your answer.

(b)  (3 marks) The price of gin is fixed at $48 per bottle, the price of plastic is $17 per tonne, and there are 27 distilleries that can produce hand sanitiser in the market. Compute the expression for the supply curve of hand sanitiser.

(c)  (4 marks) Demand in the market for hand sanitiser is initially given by Qd  = 20 − 0.2Phs . Compute the initial equilibrium price P* and equilibrium quantity traded Q* in the market for hand sanitiser. Plot the supply-demand diagram and the market equilibrium.

(d)  (4 marks) Compute the point elasticity of suddly  of hand sanitiser at the initial equilibrium price P* . Does your computation indicate that supply is elastic, inelastic, or neither? (The methods for computing the elasticity of supply are identical to the methods for computing the elasticity of demand.)

(e)  (4 marks) Demand in the market for hand sanitiser later increases to Qd  = 20 − 0.1Phs . Compute the new equilibrium price P** and equilibrium quantity traded Q** in the market. Plot the supply-demand diagram and the market equilibrium.

(f)  (4 marks) Compute the arc elasticity of suddly of hand sanitiser as the price changed from the initial equilibrium price P*  to the new equilibrium price P** .  Does your computation indicate that supply is elastic, inelastic, or neither?

(g)  (3 marks) Without computing the revenue, determine whether the increase in demand results in an increase or a decrease in the total revenue in the market for hand sanitiser. Does your answer depend on the elasticity of supply? Describe how, if it does, or explain why not, if it does not.

2. Consider the market for a certain paper product in Melbourne.   There are 5 million potential consumers of the product. Before the COVID-19 pandemic started, 2.5 million of them used a close substitute at work and did not demand the paper product.  Each of the other 2.5 million consumers had an individual inverse demand curve given by P  = 2 − 0.5q, where q is the individual quantity demanded (measured in number of packs) and P is the price in dollars per pack.  After the pandemic started, all 5 million consumers demanded the product and each one of their individual inverse demand curves was given by P = 4 − q . Market supply for the product is given by Qs  = 3, 000, 000 × P .

(a)  (3 marks) Find the total market demand before the pandemic started. (b)  (3 marks) Find the total market demand after the pandemic started.

(c)  (4 marks) Find the pre-pandemic equilibrium price and quantity.  Plot the supply- demand diagram and the market equilibrium.

(d)  (4 marks) Find the equilibrium price and quantity after the pandemic started assum- ing that supply did not change.  Plot the supply-demand diagram and the market equilibrium.

(e)  (5 marks) Alarmed by the price increase after the pandemic’s start, the Lord Mayor of Melbourne proposes an anti price-gouging law.   The law would mandate that the price of the product cannot rise more than 20% over its pre-pandemic levels. Calculate the quantity traded, the price it is traded at, and the dead-weight loss if the law is enacted.

(f)  (6 marks) Independently from the Lord Mayor, the Premier of Victoria is considering a rationing scheme.  The scheme would allow each consumer to purchase no more than a single pack of the paper product. What would the quantity traded and the dead-weight loss be if the proposed rationing scheme is enacted (and the anti price- gouging law is not)? Which of the two policies results in less inefficiency? Why?

3. The pharmaceutical conglomerate Pfizeneca has discovered a new vaccine for COVID- 19, called  covbegonium.   The vaccine is subsequently approved in Australia and New Zealand so Pfizeneca can sell its vaccine there. In Australia, demand for covbegonium is QAU  = 20.5 − PAU , where QAU  is the quantity demanded when the price in Australia is PAU .  In New Zealand, demand for covbegonium is QNZ  = 5 − PNZ , where QNZ  is the quantity demanded when the price in New Zealand is PNZ , denominated in Australian dollars. (All monetary amounts in this problem are given in Australian dollars.) Pfizeneca has a single manufacturing plant in Australia and its marginal cost is constant at $10. In this problem you can ignore the cost of transporting covbegonium from the site of manufacture to consumers, regardless of where they are located.

(a)  (6 marks) Assuming that Pfizeneca can successfully charge different prices in Aus- tralia and in New Zealand, what profit-maximising prices PAU   and PNZ  would it charge in each of the two countries? What quantity of covbegonium would it sell in each of the two countries? Provide intuition for your answer.

(b)  (7 marks)  Covbegonium  is later approved for sale in Canada as well.   Canadian demand for covbegonium is QCA  = 20.5−PCA , where QCA  is the quantity demanded when the price in Canada is PCA . Assuming that Pfizeneca can successfully charge different prices in Australia, in Canada, and in New Zealand, what profit-maximising prices PAU , PCA , and PNZ  would it charge in each of the three countries?  What quantity of covbegonium would it sell in each of the three countries?

(c)  (6 marks) After building a second manufacturing plant in New Zealand, Pfizeneca can now produce covbegonium at either or both of its manufacturing plants.  The marginal cost of producing covbegonium at the new plant is 0.1Q, where Q is the total quantity of covbegonium  produced at the plant.  The marginal cost at the old plant remains $10.  At the same time, Pfizeneca finds itself temporarily unable to sell covbegonium in Canada due to import restrictions.  Assuming that Pfizeneca can successfully charge different prices in Australia and in New Zealand, what profit-maximising prices PAU   and PNZ   would it charge in each of the two countries? What quantity of covbegonium would it sell in each of the two countries? How much would Pfizeneca produce at each of its plants and why?  (Hint 1:  You may want to think about the last question first. Hint 2: Using the profit-maximising condition for Pfizeneca, you may want to express QA(*)U  as a function of QN(*)Z , where Q ··(*)  denotes the profit-maximising quantity for the respective country.)

(d)  (6 marks) Eventually, Canadian import restrictions are lifted and Pfizeneca can sell covbegonium there again. Assuming that Pfizeneca can successfully charge different prices in Australia, in Canada, and in New Zealand, what profit-maximising prices PAU , PCA , and PNZ  would it charge in each of the three countries? What quantity of covbegonium would it sell in each of the three countries? How much would Pfizeneca produce at each of its plants and why? Why did the profit-maximising quantity sold in New Zealand change relative to part (c)?