Question

U=100x 68 z02 The price of X is px =$5, the price of Z is p2 =$10, his ineome is $1,200, his MUX =80X−02 Z02 , and his MUZ =20X08 Z−03

What is Diogo's oplimal bunde? (round your Atswer to one decimtar place) x0 =192 units zs =24 units
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Answer 1

To determine Diogo's optimal bundle, we need to maximize his utility subject to his income constraint. Diogo's utility function is given as MUX = 80X - 0.2Z and MUZ = 20X + 0.8Z, where X represents the quantity of good X and Z represents the quantity of good Z. Based on the given prices and income, we can calculate the budget constraint and set up an optimization problem.

Step-by-step explanation:

To determine Diogo's optimal bundle, we need to maximize his utility subject to his income constraint. Diogo's utility function is given as MUX = 80X - 0.2Z and MUZ = 20X + 0.8Z, where X represents the quantity of good X and Z represents the quantity of good Z.

Based on the given prices and income, we can calculate the budget constraint and set up an optimization problem.

1. First, calculate the total cost of good X and good Z by multiplying their respective prices with the quantities given: Total cost of good X = $5 * 192 units = $960 and Total cost of good Z = $10 * 24 units = $240.
2. Next, set up the optimization problem. Maximize MUX = 80X - 0.2Z subject to the budget constraint: 5X + 10Z ≤ $1200.
3. Using the optimization problem, solve for the optimal quantities of X and Z. The solution should give you the values for X and Z that maximize Diogo's utility within his budget constraint.