The utility function of a certain good is given by U(x) = 60x - x2 where x represents the number of units produced and sold during a month. How many units must be produced and sold to maximize utility? What is the maximum utility?
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The utility function of a certain good is given by U(x) = 60x - x2 where x represents the number of units produced and sold during a month.
How many units must be produced and sold to maximize utility? What is the maximum utility?
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- 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.Utility is a type of function that occurs in economics. When a consumer receives x units of a certain product, a certain amount of pleasure, or utility U, is derived. The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is. (Type an integer or a decimal.) C Utility (pleasure units) AU 200- 150- 100- 50- 0 (1,67) (2,106) I (3,134) (4,156) 2 Number of units of product 4 XConsider the utility function: U(x,y)= -4(3x-12)² - (2y-10)² Determine the marginal utility for the two commodities
- (Review Question) Sarah consumes both wine ) and cheese (y) and considers them perfect substitutes. She always gets twice as much utility from consuming wine as she does cheese. What equation would represent her utility function? U-(2xy) U=x+2y U=2x+y U=min(x,2y)A utility function is given by the equation U = 20xe¬0.1x, where x is the number of glasses of wine consumed. (a) Show that this utility function has a maximum value and calculate the maximum utility. (b) Describe how marginal utility changes for glasses of wine consumed after the maximum utility is reached. Do you consider this reasonable? Give an explanation.The utility function of a consumer is u = √x + 2y. (a) Calculate how much MRS of that consumer when x = 4. (b) If the consumer currently consumes 4 units of goods x and the price ratio of Px / Py = 1/4, then the consumer should increase or decrease the consumption of goods x?
- For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +XbThe marginal utility derived from the consumption of extra unit of commodity. True/FalseA consumer has the following utility function: U(X,Y)= 400X2/5Y3/5 Suppose that the price of a spa day (x) is £200 and the price of a city break (y) is £300 Find the number of spa days and city breaks that minimise expenditure if 12,800 units of utility are obtained. Also calculate the consumer's minimised expenditure
- A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 250 units. For each additional $2500 spent, an additional 25 units are sold. 1. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x. y= 2. How many units does the firm sell if it spends $25,000 on advertising? = ____ units 3. How many units does the firm sell if it spends $50,000 on advertising? = ____ units 4. How much advertising money must be spent to sell 700 units? = _____$ 5. Which of the following statements CORRECTLY explains the meaning of the slope? (select all as there may be more than one correct statment) A. If the company spends an additional $1000 on advertising, it will increases the number of units it sells by 10 . B. If the company increases the amount of money it spends on advertising by $250, it…A consumer attains maximum utility when: Select one: a) Marginal utility per dollar spent is positive for every good purchased b) Marginal utility per dollar spent is increasing for every good purchased c) Marginal utility per dollar spent is same for every good purchased d) Marginal utility per dollar spent is negative for every good purchased e) Marginal utility per dollar spent is decreasing for every good purchasedIf the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.
