Figure 5-1 shows the preferences of a consumer for food and other goods. He is initially in equilibrium at point A where the budget line MN is tangent to the indifference curve. From the initial point of equilibrium, an excise subsidy will move the consumer to point
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- The rules of politics are not always the same as the rules of economics. In discussions of setting budgets for government agencies, there is a strategy called closing the Washington Monument. When an agency faces the unwelcome prospect of a budget cut, it may decide to close a high-visibility attraction enjoyed by many people (like the Washington Monument). Explain in terms of diminishing marginal utility why the Washington Monument strategy is So misleading. Hint: If you are really trying to make the best of a budget cut, should you cut the items in your budget with tile highest marginal utility or line lowest marginal utility? Does the Washington Monument strategy cut the items with the highest marginal utility or line lowest marginal utility?5. Consider a consumer whose utility function isu(x,y) = sqrt(xy) (MRS(x,y)=y/x)a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. Howmuch x and y would they buy? Draw the budget constraint and the demands. b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw thisin the same figure.c. Decompose the total effect of the price change on demand for x into the substitution effect and theincome effect. That is, determine precisely how much of the change is due to each of thecomponent effects. (Hint: See the lecture notes for the two properties that determine the locationof “z”, the reference point for distinguishing the income and substitution effects.)The utility function is U(x1x2) = x1(x2 - 2), x1 >= 0, x2 >= 2. The consumer receives a subsidy of 1 m.u. for each unit he buys of the first good while he must pay a 5% tax for the entire value of second good. He is also subject to a 20 m.u. tax for his entire income. Comment the new opt. point, the new budget line and the change in the affordable set. Use I = 500, p= (2 2) as initial values).
- 9) Jonathan spends his income (M) on good X and Y. His preferences are represented by theutility function(X, Y) = Ln X + LnY.The price of good Y is 1 and the price of good X is PX.(a) Derive his demand for X and Y. (b) Jonathan’s father considers X and Y as merit goods and wants to encourage his son toconsume more of them by offering him a subsidy of $1 for every unit of X that hepurchases. Suppose the initial price of X is $2, derive the substitution effect ofJonathan’s demand for X with the subsidy when his income is $20.(c) Does the subsidy increase Jonathan’s consumption of Y?(d) How does the subsidy affect Jonathan’s total spending on X and Y.(e) Instead of offering the subsidy, the father decides to spend the same amount of moneyon Jonathan by offering him an income supplement. Is this a better alternative thanthe unit subsidy in achieving the father’s objective? 12(a) Consider a perfectly competitive industry with several identical firms.The cost function of a price-taking firm…1. Suppose that a consumer’s utility function for two goods (X and Y) is U(X,Y) = 10X^0.5 + 2Y , with MUx = 5X-0.5 and MUy = 2. The price of good X is $5 per unit, the price of good Y is $10 per unit, and the income is $275. a. Find the utility maximizing quantities of X and Y. b. If instead, the price of good Y is $20 per unit, how does your answer change?3(b)Discuss, using indifference curve analysis, why a decrease in a sales tax on all goods and services might have a different impact on demand for a normal good than for an inferior good. include all relevant graphs too.
- 2. The demand for good X is given by:d= 6,000 - 0.5Px - Py +9Pz + 0.1MQxResearch shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while theaverage income of individuals consuming this product is M = $70,000.a. Indicate whether goods Y and Z are substitutes or complements for good X.b. Is X an inferior or normal good?c. How many units of good X will be purchased when Px = $5,230?d. Determine the demand function and inverse demand function for good X. Graph the demand curve forgood X.17. The general demand function for good A is Qd = 754 − 2PA − 0.05M + 6PB +10ℑ+ 3PE + 2N where Qd = quantity demanded of good A each month, PA = price of good A, M = average household income, PB = price of related good B, ℑ = a consumer taste index ranging in value from 0 to 10 (the highest rating), PE = price consumers expect to pay next month for good A, and N = number of buyers in the market for good A. a. Interpret the slope parameter for income. Is good A normal or inferior? Explain. b. Are goods A and B substitutes or complements? Explain. Interpret the slope parameter for the price of good B. c. Are the algebraic signs on the slope parameters forℑ, PE, and N correct? Explain.A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.
- 6. My utility over goods 1 and 2 is given by: u(x1,x2)=min{x1/a,x2/b} Where x1is the quantity of good 1 I consume and x2 is the quantity of good 2 I consume. Assuming I purchase only goods 1 and 2... If a = 2, b = 5, the price of good 1 is $2/unit, the price of good 2 if $7/unit and my income is $5, how much good 2 will I consume to maximize my utility? (Note: The answer may not be a whole number, so round your answer to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)7.If pizza is a normal good, then which of the following could be the value of incomeelasticity of demand?(2marks)a) 0.2.b) 0.8.c) 1.4d) All of the above.(a) A good is a luxury if it has a budget elasticity larger than 1, (i.e., good k is a luxury if εk ≡∂qk/∂m *m/qk> 1). Show that when a good is a luxury, then if a consumer’s total budget rises, theywill raise the share of their budget they allocate to the good. (b) Suppose m is the total budget a consumer has available to spend on three electronic products,a laptop, a phone and a tablet. Can all three of these goods simultaneously be luxuries? Whyor why not?
