0.5, Utility function is given as Cobb Douglas functional form: U = x1.5x2.5 Price the first good: P₁ = 5$ Price the second good: P₂ Income: I = 500$ = 10$
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- The demand function for a particular good is x = a + bp. What are the associated direct and indirect utility functions?A consumer has the following demand function for good 1: x1 = (1/4)(m/p1) The original price of the good is $2 and the consumer’s income is $200. Calculate the substitution effect, the income effect and the total effect for this consumer, when the price of good changes to $1.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to find that of Y) when your preferences are represented by the utility function U = x + xy + y. Is X normal good? Can you confirm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived
- What is the difference between good x as a function of price and income and good x as a function of price and utility?The utility of a consumer derives from consuming the two goods X and Y can be assumed to be determined by the utility functionU(X,Y)= 4X03Y05. If good X costs 10 birr a unit and good Y costs 15 birr a unit and the consumer's income is 120 birr. What combination of X and Y that will maximize utility?0.8 A consumer's utility function is given by the expression: U = (0.6X0.5 +0.4Y0.5) ². Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
- A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizzaConsider the following utility function that expresses the preferences of any consumer for good x and good U(x, y) Min {2x, y) Consider that the price of x is $4, the price of y is $2, and the income R is $100. Reply: a) What is the marginal rate of substitution for x? b) What is the marginal rate of substitution for y? c) What is the expression of demand ( demand function) of x? d) What is the demand expression (demand function) for y? e) What is the basket composition that maximizes this consumer's satisfaction given the given restriction? f) What is the utility achieved with this basket?Question 2 Emma's daily utility function is U = 8√R+ 4M, where R represents the pounds of rice eaten in a day and M represents the money spent in other food. Marginal utility for rice and other food is: MUR = 4R-, MUM = 4. (a) Assume price for rice is pr, price for other food is pm and Emma's income is m. Derive the demand function given prices Pr Pm and income m. (b) Assume initially the price for rice is $0.5 per bowl. The price of other food is $1. Emma's daily income is $10. How much R and M will she buy? (Don't round off fractions) (c) Now the price of rice increases to $1 per bowl. The price of other food is still $1. Emma's daily income is still $10. How much R and M will she buy now?
- The utility function of a consumer is given as follows. U(x, y) = x²y³, MU, = 2xy3 and MU, = 3x?y?. a. Derive the demand functions for good x and good y. b. Draw a demand curve. Draw an Engel curve. Is good x a normal good? С.Which of the following is not a required characteristic for a function U(.) to be considered a valid utility function? (Select all that apply) U(.) must be monotonically increasing in all possible bundles U(.) must be able to assign a utility to every possible bundle of goods For any two bundles, A and B, either U(A) ≥ U(B) or U(B) ≥ U(A) must be true For any three bundles, A, B, and C, if U(A) ≥ U(B) and U(B) ≥ U(C), then U(A) ≥ U(C)Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…