The demand for wheat in a country is QD = 200 − 2P, and supply is QS = −20 + 2P, where P is price in pounds and Q is quantity in tonnes. (a) Find the no-trade equilibrium price and quantity in the market. What are the values of consumer and producer surplus in equilibrium? (b) The government decides to open the domestic market to imports. The world price of wheat is £20 per tonne. In order to safeguard farming the government sets a tariff of £20 per tonne. Illustrate on a diagram and calculate the government’s revenue from the tariff. (c) Calculate the new consumer surplus and producer surplus under (b). By how much is society better off than under (a) above? Comment on the implications for the distribution of income between farmers and consumers if the tariff revenue is given to farmers as a lump sum payment. 2. Discuss the following questions and substantiate your arguments with economic theory. Clearly state which assumptions you make in answering the questions. Make use of diagrams where appropriate. (a) You are charged with maximising governmental revenues from cigarette taxation. What kind of tax rate do you propose and why? Is it possible that you would advise the government to reduce the tax rate? Why or why not? (b) Discuss possible reasons why a government that wants to increase tax revenues would like to tax cigarettes at all. Are there other goods you think that revenue-maximising governments would like to tax? Why? (c) How would your answer to (a) change if in addition to generating revenues, the government would also like to make people healthier? 3. In a perfectly competitive market, the demand curve is QD = 120 − 3P and the supply curve is QS = 2P, where QD is the quantity demanded, QS is the quantity supplied, and P is the price. 1(a) Find the equilibrium price and quantity. Calculate consumer and producer surplus in this market. (b) The government now introduces a tax of T = 10 per unit sold, so that the supply curve now becomes QS = 2(P − T), where P is the price paid by consumers. Calculate the government’s revenue from the tax. (c) Find the deadweight loss associated with the tax. How else could the government in this example raise the same tax revenue, without incurring any deadweight loss? 4. In a competitive market, market demand is q d = 104 − 16p, where q d denotes the quantity demanded and p is the price. Market supply is q s = 8p − 16, where q s denotes the quantity supplied. (a) Explain why at the equilibrium it must be true that demand equals supply. Calculate the equilibrium price and quantity in the market. Show your result diagrammatically. (b) Explain the concepts of consumer and producer surplus. Use your results in (a) to calculate producer and consumer surplus in this economy. (c) Now suppose the government introduces a specific tax, t = 3 paid by the suppliers. Find the new equilibrium price and quantity in the market and compare your result to your result in (a). Show your result diagrammatically. (d) Using a diagram to illustrate your answer, explain how the introduction of a specific tax creates a deadweight loss in the market. Explain how this deadweight loss depends on the elasticity of demand. 5. Assume that the UK changes planning regulations to the extent that it becomes easier to build new houses. Making use of economic theory and diagrams where appropriate, discuss the effect of this regulatory change on the following: (a) The price of houses for first-time buyers. Clearly state any assumptions you make in your answer. (b) The demand for country houses adjacent to new housing developments. Clearly state any assumptions you make in your answer. (c) Does your answer to (b) depend on whether new houses are accompanied by better infrastructure (e.g., shops, road, schools, etc.)? Clearly state any assumptions you make in your answer. 6. Consider a consumer with utility function U(x, y) = 2x + y. The price of good x is px = 10, which is identical to the price of good y, py = 10. The total income of the consumer is given by M = 500. (a) Derive the Marginal Rate of Substitution between goods x and y and solve for the optimal consumption bundle. 2(b) Show the solution in a graph. What level of utility is the consumer going to achieve with this bundle? (c) Now assume that the price of good y decreases to 5. Find the new optimal consumption bundle and comment on it. (d) Find the income and substitution effects associated with the decrease in the price of y. Explain your finding. 7. Jim has an income of £100 which he spends on two goods, beer and pizza. The price of beer is £2 per unit and the price of pizza is £2 per unit. Assume that Jim behaves optimally. (a) Write down Jim’s budget constraint. Draw a diagram of Jim’s budget line with pizza on the horizontal axis. Jim consumes 30 pizzas. How many beers does he consume? (b) Now the price of pizza falls to £1 per unit and Jim consumes 50 pizzas. The price of beer and Jim’s income are unchanged. Jim tells us that with the pizza price at £1 he would be just as well off as he was originally (under (a) above) if he had an income of £70, in which case he would consume 40 pizzas. Use this information to calculate the substitution and income effects of the fall in the price of pizza from £2 to £1. (c) Is beer a normal good for Jim? Explain. 8. John’s utility function is given as: U(x, y) = xy, where x and y denote the quantities of goods x and y he consumes. His budget constraint is: 4x + 8y = 120, where 4 is the price of good x, 8 is the price of good y and 120 is his income. (a) From the utility function find the expression of the Marginal Rate of Substitution for John. Find the typical equation of an Indifference Curve for John. (b) Find the optimal quantities for x and y consumed by John. Show your solution diagrammatically. (c) John’s friend Anne has exactly the same income as John. However, Anne’s utility function is U(x, y) = x 1
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