Manuel has the following utility U(91, 92) = 2591595. For what values of q: and q2...

 

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Manuel has the following utility U(91, 92) = 2591595. For what values of q: and q2 do the two marginal utilities equal 0? Is that a maximum or a minimum? Which combination of q₁ and 2 provides him with the maximum level of utility? 3.2 Now suppose prices are p₁ = 5 and p2 = 10 and that Manuel has $100. Write Manuel's budget constraint and graph it with q₁ in the x-axis. What is the slope? And the intercept? What is the maximum amount of q, he can purchase? And the maximum amount of q2 he can purchase? 92 3.3 Next, we will find out the best use Manuel could make of his money, given his preferences. Based on Manuel's preferences, let's figure out the ratio between 91 and 92. What is the ratio of the two marginal utilities (MRS)? (remember that MU₁ is in the numerator) 3.4 Now we have the ratio of how Manuel trades both goods. We will equalize it to the ratio of both prices. That is, how Manuel trades both goods needs to equal how the market trades them. In the optimal bundle, what is the relationship between 9₁ and 92? (Condition for optimality) 3.5 Finally, use the previous relationship to substitute in the budget constraint and find the optimal quantities of 1 and 92, which we denote by qi and q2. Manuel has the following utility U(91, 92) = 2591595. For what values of q: and q2 do the two marginal utilities equal 0? Is that a maximum or a minimum? Which combination of q₁ and 2 provides him with the maximum level of utility? 3.2 Now suppose prices are p₁ = 5 and p2 = 10 and that Manuel has $100. Write Manuel's budget constraint and graph it with q₁ in the x-axis. What is the slope? And the intercept? What is the maximum amount of q, he can purchase? And the maximum amount of q2 he can purchase? 92 3.3 Next, we will find out the best use Manuel could make of his money, given his preferences. Based on Manuel's preferences, let's figure out the ratio between 91 and 92. What is the ratio of the two marginal utilities (MRS)? (remember that MU₁ is in the numerator) 3.4 Now we have the ratio of how Manuel trades both goods. We will equalize it to the ratio of both prices. That is, how Manuel trades both goods needs to equal how the market trades them. In the optimal bundle, what is the relationship between 9₁ and 92? (Condition for optimality) 3.5 Finally, use the previous relationship to substitute in the budget constraint and find the optimal quantities of 1 and 92, which we denote by qi and q2.

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1To find the values of q and 9 for which the two marginal utilities equal 0 we need to take the part... View the full answer