Suppose utility for a consumer of movies (x) and golf (z) is U = 20x0.6z0.4. The consumer has...

Suppose utility for a consumer of movies (x) and golf (z) is U = 20x^0.6z^0.4. The consumer has set aside $1000 to consumer movies and golf for a year.
1. If the price of movies is $20 and the price of golf is $30, what is the utility-maximizing consumption of movies and golf? (Use demand functions formula to solve).
2. Show the optimal consumption bundle on a graph, showing a budget line (with intercepts), an indifference curve, and the optimal choice.
3. Now suppose the price of golf falls to $25. What is the new utility-maximizing consumption of movies and golf?
4. Show the new situation on your graph, including the new BL (with intercepts), new indifference curve, and new optimal choice. Also, show the price-consumption line.
5. What is the price elasticity of demand for golf? To calculate, use the midpoint method, where percentage change for a variable x is (change in x)/(average x).

Expert Solution

Rahul Sunny answered 1 year ago

Suppose utility for a consumer of movies (x) and golf (z) is U = 20x0.6z0.4. The...

Suppose utility for a consumer of movies (x) and golf (z) is U = 20x0.6z0.4. The consumer has set aside $1000 to consumer movies and golf for a year. If the price of movies is $20 and the price of golf is $30, what is the utility-maximizing consumption of movies and golf? (Use demand functions formula to solve). Show the optimal consumption bundle on a graph, showing a budget line (with intercepts), an indifference curve, and the optimal choice. Now...

2. Suppose utility for a consumer of cereal (x) and milk (z) is U = min(x,...

2. Suppose utility for a consumer of cereal (x) and milk (z) is U = min(x, 2z), where 2 boxes of cereal are consumed with one carton of milk (x=2z). a. What is the optimal consumption bundle if $42 are allocated to cereal and milk over a 6-month period, and the price of cereal is $3 and price of milk is $2? b. Graph the situation, including indifference curves, budget line, and the optimal choice.

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.

Suppose that a consumer has utility given by U(X, Y ) = XY + 10Y and...

Suppose that a consumer has utility given by U(X, Y ) = XY + 10Y and income of $100 to spend on goods X and Y. The prices of X and Y are both $1 per unit. Use a Lagrangian to solve for the optimal basket of goods. Suppose that the price of X increases to $5 per unit. Use a Lagrangian to solve for the new optimal basket of goods. Find the total effect of the price change on...

Suppose a consumer has a utility function given by u(x, y) = x + y, so...

Suppose a consumer has a utility function given by u(x, y) = x + y, so that the two goods are perfect substitutes. Use the Lagrangian method to fully characterize the solution to max(x,y) u(x, y) s.t. x + py ≤ m, x ≥ 0, y ≥ 0, where m > 0 and p < 1. Evaluate and interpret each of the multipliers in this case. What happens to your solution when p > 1? What about when p =...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x and y are the quantities of the good X and good Y consumed, respectively. The consumer's income is 400. (a) What is the demanded bundle when the price of good X is 10 and the price of good Y is 10? (b) Redo part (a) when the price of good X is doubled? (c) Redo part (a) when the price of good Y is...

Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY =...

Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY = 1, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values PX = 1, PX = 2, and PX = 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference...

"Suppose a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py =...

"Suppose a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py = 1, and the consumer has $360 to spend. Draw the Price-Consumption Curve for this consumer for income values Px =1, Px = 2, and Px = 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also for each bundle that the consumer chooses, draw the indifference curve...

Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $200...

Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $200 to spend, and the price of X, PX = 5, and the price of Y, PY = 2. a) How much X and Y should the consumer purchase in order to maximize her utility? b) How much total utility does the consumer receive? c) Now suppose PX decreases to 1.25. What is the new bundle of X and Y that the consumer will demand?...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY. a. Find the consumer’s marginal utility of X (MUX) and marginal utility of Y (MUY). b. Find the consumer’s marginal rate of substitution (MRS). c. Derive the consumer's demand equations for both goods as functions of the variables PX,...

Question