Suppose there are 2,000 potential consumers in the Chestnut Hill market for tablet computers. All consumers have identical preferences over tablets (T) and expenditures on other consumption goods (X), represented by the following utility function: U(T, X) = 500T(1 – T) + a) Find the total market demand for T (call it TM) as a function of the price of a tablet (pT ). b) Write down the equation for the market demand curve (with TM on the horizontal axis and pT on the vertical axis).
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- Suppose there are two agents Ahmet and Berk in an economy, and both consume two goods X and Y. Also assume that price of X is 2 YTL and Y is the numeraire good, thus price of Y is 1 YTL. Ahmet and Berk has the following utility functions:UAhmet (XA,YA)= 5ln(XA)+ln(YA)UBerk (XB,YB)= XB0,5 YB0,5a. Now assume that both X and Y are private goods. Write down the optimality condition for both agents. Then, write down the optimal level of X as a function of Y for both agents.b. Now assume that X is a public good, but Y is a private good. Write down the optimality condition for good X. Then, write down the optimal level of X as a function of Y for both agents.c. Now compare the consumption levels for X in parts a and b.A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility functionU (x, y) = 10x0.6y0.4a. How many units of each commodity should the consumer buy tomaximize utility?b. Is the budget constraint binding?Suppose that the utility function U(C, S) = C + 2S^1/3 describes Molly’s preferences over two goods:Carrots (c) and Spinach (s). Give another utility function that represents Molly’s preferences just as well as the one given above. Justify your answer by showing that your new utility function has the same formula for MRS as the given one.
- 4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…Suppose NUL students have a monthly income of M1,100, and they allocate half of this amount among two goods; Eggs and Yogurt. Suppose a tray of eggs costs M55 while yogurt costs M22 per case. Suppose Bongile has preference over Eggs (E) and Yogurt (Y) given by the following Cobb-Douglas utility function: U ( E,Y )=E^0.5 Y^2 Given initial prices of eggs and yogurt, and income allocated on both commodities, find the optimal utility maximizing consumption bundles (E*, Y*).
- Jack derives utility from Hokey course (H) and Chess course (C) as given by the following utility function:U (H, C) = √HCThe average price for the hokey course is 20 dollars and for chess course16 dollars. Moreover, Jack has a budgetof 80 dollars. c) Find the income level which is necessary to make Jack reach the same utility level as before theprice change.d) Compute the quantities demanded with the new prices and the income you found in section c.e) Compute the quantities demanded with the new prices and the original budget of 800 dollars.Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)− according to the Cobb-Douglas utility function U(x,y,z)=x0.5y0.5(1+z)0.5. Suppose also that the prices for these goods are given by px=1,py=4, and pz=8 and that this consumer's income is given by I=8.a. Show that, for z=0, maximization of utility results in the same optimal choices as in Example 4.1 . Show also that any choice that results in z>0 (even for a fractionalz ) reduces utility from this optimum.b. How do you explain the fact that z=0 is optimal here?c. How high would this individual's income have to be for any z to be purchased?27. Mike spends all his income on films (F) and concerts (C). Films cost $10 and concertscost $30. Mike’s preferences can be described by the utility function: U = F C and hence themarginal utility of films is C and the marginal utility of concerts is F. Which of the followingbundle will Mike purchase? (Hint: You do not need to know income in $ amount. Answerthe question using the tangency condition.)(a) Mike purchases 30 concerts and 10 films a month.(b) Mike purchases 10 concerts and 30 films a month.(c) Mike purchases 20 concerts and 20 films a month.(d) Mike purchases 5 concerts and 10 films a month.