Suppose that consumer has the following utility function: U(X,Y) = XY and Px = 1, Py = 4 and I = 720. Suppose now that Px goes up to 4. What is the magnitude of the substitution effect on good X? -90 180 -180
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- An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week. Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute 4 pounds of a generic store brand for 2 pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?Suppose that consumer has the following utility function: U(X,Y) = XY and Px = 1, Py = 4 and I = 720. Suppose now that Px goes up to 4. What is the magnitude of the income effect on good X? %3D O -180 90 180 O-90
- 5. 24.A large Coca-Cola vendor recently hired some economic analysts to assess the effect of a price increase in its 16-ounce bottles from $1.00 to $2.00. The analysts determined that, on average, the vendor's customers spend about $15.00 on soda (Coke and all other brands) each week, and the average price for other 16- ounce soda bottles is $1.00. The analysts also utilized some focus groups to determine the preferences of the vendor's customers. They used this analysis to build the following graph: Bottles of Budget line with price of $1.00 Other Soda Budget line with price of $2.00 Bottles of Coke Suppose Xo = 9 and X1 = 7. Should the vendor expect to sell 7, more than 7, or less than 7 bottles of Coke after raising the price to $2.00 if Coke is a normal good?The marginal utilities derived from the consumption of goods X and Y by a given consumer are given by MUx=40-6x and MUy=80-10y. If the prices of X and Y are Gh2 and Gh10 respectfully. determine the number of units of the commodities that the consumer must consume to optimize satisfaction granted that he/she earns an income of GH40 within the period.Calculate the marginal rate of substitution (MRS12) for the following utility function: U(91, 92) (1491 +692)³. What is the value of MRS12 at bundle (4, 8)? Please round your answer to two decimal places if necessary.
- 7. An individual's utility function is given by U =1000x, +450x, +5 x,x, -2x - x where x, is the amount of leisure measured in hours per week and x, is income earned measured in cedis per week. Determine the value of the marginal utilities, when x, = 138 and x, = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?Find the marginal rate of substitution given the following utility functions for x and y: U(x) = 2xy U(y) = 3x1/3,2/3 O x1/3 / yA/3 O 213 x213y1/3 y2/3 / x1/3 'yA/3 /x1/3Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} 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.
- Q.7 A consumer's utility function is given by the expression: U = (0.6Xx5 + 0.4Y5). • 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.Total Utility derived from the consumption of a product to a consumer is given by U = (20-0.50)'Q where Q is the number of units consumed Using a graphical representation, show what is the nature of variation in the utility with the increasing consumption of the product? Is it in line with the law of diminishing marginal utility? Explain.Stuart's utility function for goods X and Y is represented as U(X,Y)=X0.8Y0.2. Assume that his income is $100 and the prices of goods X and Y are $20 and $10, respectively. Now a government subsidy program lowers the price of X from $20 per unit to $10 per unit. (a) Calculate and graphically show the change in good X consumption resulting from the program. (b) Graphically show the change in consumption attributable to the separate income and substitution effects. (c) Show (graphically) how much the program cost the government.
