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- Suppose that the utility function for two goods X and Y is given by U = x2y. (a) Write the equation of the indifference curve for a consumer who purchases 8 units of X and 25 units of Y. (b) If the consumer purchases 100 units of Y, how many units of X must be purchased to retain the same level of utility?Suppose the demand functions for two products are q1 = f(p1, p2) and q2 = g(p1, p2) wherep1, p2, q1, and q2 are the prices (in dollars) and quantities for products 1 and 2. Consider thefour partial derivatives∂q1/∂p1,∂q1/∂p2,∂q2/∂p1and ∂q2/∂p2,State the sign of each of these partial derivatives if:(a) the products are complementary goods(b) the products are substitute goods.Pete consumes goods 1 and 2. Pete thinks that 3 units of good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions is the only one that would not represent Pete's preferences? A B с D E U (x₁,x₂) = 40x₁+30x - 10000 1 2 U (x₁,x₂) = 4x₁+3x₂+ 1000 1 2 U(x,x) = min(4x, 3x₂) U (x₁,x₂) = 16x² + 24x x₂ + 9x² 12 More than one of the above does not represent Pete's preferences.
- The supply and demand equations of a good are given by the following formulas P=2Qs +48 P= -6QD+ 160 Find the equilibrium price and quantity. The equilibrium quantity is. (Type an integer or a decimal.) ***1. Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F, C) = F 1/3 C 2/3 . Roy has the utility function V (F, C) = F 2/3 C 1/3 . Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto efcient allocation of F and C between the two con sumers? Explain briefy. (b) What is each consumer’s demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 + 9P.] (c) What is the price of C in a competitive equilibrium? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium?Applying the DDM model utilizing the following inputs: PO, d1, d2, r, g. When rearranging the price expression so that we can solve for g, g= r - d2/((PO*(1+r)-d1)) True False
- D6) if the price elasticity of demand for a good is greater than three, Dan the demand for that good is? a. perfectly elastic b. elastic c. inelastic d. unit elastic6. p= ($20, 0.4; $40, 0.6). Use a concave utility function to graphically illustrate each of the following: a. Show that EU(p) > EU(q) where q is a mean-preserving spread of p. (Note: This will work for any lottery q. Choose one to illustrate.) b. Show that EU(r) > EU(p) where r is a non mean-preserving spread of p. (Note: This won't work for all lotteries r. Find one that does work.)Consider an individual facing the prospect of having high income, YH > 0, with probability 7 and low income, YL, with probability 1 – T, YH > YL. Prior to learning whether realized income is high or low, the individual is able to go into the market and purchase (or sell) two types of assets. Let the Asset 1 have a return structure such that it pays R1.H units of goods if y = YH and pays R1,L units of goods if y = YL. Similarly, let Asset 2 have a return structure such that it pays R2.H units of goods if y = YH and pays R2,L units of goods if y to spend in the asset market but this wealth is not storable and hence cannot be save to purchase consumption goods. Denote by a1 the amount of Asset 1 purchased by the individual and az the amount of Asset 2 purchased by the individual. The individual's problem is to maximize the expected utility from consumption sub- ject to the constraints that consumption must be financed out of income and the realized return from the asset portfolio as well…
- Find the marginal profit function if cost and revenue are given by C(x) = 224 + 0.8x and R(x) = 8x – 0.05x2. P'(x) =DHydro Ottawa has two options for upgrading a natural gas power station to meet new government standards. Option 1: Hydro Ottawa will make the upgrades themselves. This is expected to cost $12,700 at the end of each month for 12 years. At the end of the operation (in 12 years) Hydro Ottawa expects to sell all equipment needed for the upgrade for $122,000. Option 2: Pay experienced contractors. This will cost $28,000 up front and $13,900 monthly (at the end of every month) for 15 years. Assume all interest is 3.72% compounded monthly. Round the answers to NPV (Option 1), and NPV (Option 2) to the nearest dollar. Round all other answers to two decimal places where applicable. 1) Find the net present value of option 1: P/Y = C/Y = N = I/Y = PV = PMT= FV = Payments (Cost) GA % Sale of equipment (Residual) GA GA LA %State the decision criteria for each of the following. (2) PI > MIRR > NPV > IRR > options; 0 1 PI MIRR NPV IRR Payback