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U = 8x10.5+ 2x2, where x1 is the quantity of good 1 consumed, and x2 is...

U = 8x10.5+ 2x2, where x1 is the quantity of good 1 consumed, and x2 is the quantity of good 2 consumed. (Yes the x is raised) 8x1.5

Suppose that the consumer has a budget of M = $400 to spend and that good 1 has a price of p1= 2, and good 2 has a price of p2= 8.

Answer the following questions, and write your answers in the Answer Sheet.

  • Write the person’s budget constraint as an equation, with two variables (x1 and x2).

  • Write the utility maximization problem. This involves rewriting the utility function with the budget constraint substituted in.

  • Find the first-order condition.

  • Find the combination of goods (x1 and x2) that maximizes the consumer’s utility at these prices.

    • What is the optimal x1?

    • What is the optimal x2?

      Budget Constraint Equation 400 = 2x1 + 8x2
      Utility Maximization Problem Max U = 8x10.5 − 0.5x1 + 100
      First-order condition

      4x1−0.5 − 0.5 = 0
      Optimal x1 x1=
      Optimal x2

      x2=
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Answer #1

Hue utility fruction jor. U= 8x,0.5 + 2X2 aget of m= ice of 4400, also, good X2 i PL Now, the con sues has a budget of m= 440Budget constraint Equation 400 = 2x1 + 8X2 Utility Manimization Problem L= 84,014 2X2 + 1 [460- 2X1 - 8 X first-order Conditi

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