$10.$ Deriving demand from an indifference map

Susan recently moved to Chicago, where they developed a taste for drinking Americanos and eating danishes. Assume throughout this problem that the price of an Americano is held constant at $\backslash$$$4.$

On the following graph, the purple curves $(\backslash (\backslash$mathrm$\{$I$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$I$\}\_\{2\}\backslash ))$ describe two of Susan's indifference curves. The lines $\backslash (\backslash$mathrm$\{$BC$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$BC$\}\_\{2\}\backslash )$ represent two budget constraints. Points X and Y show Susan's optimal consumption bundles subject to the budget constraints.

Given the preceding graph and knowing the price of an Americano is $\backslash (\backslash$$ $4\backslash ),$ Susan's available income for Americanos and danishes is $\backslash (\backslash$mid $\backslash )$ Using the income amount you just computed, complete the following table by finding the price of a danish when $\backslash (\backslash$mathrm$\{$BC$\}\_\{1\}\backslash )$ represents Susan's budget constraint and when $\backslash (\backslash$mathrm$\{$BC$\}\_\{2\}\backslash )$ represents her budget constraint. Then indicate the quantity of danishes consumed in each of those scenarios.

Price

Consumption

When Susan's budget constraint is$...$

$($Dollars per danish$)$

$($Danishes$)$

$\backslash (\backslash$mathrm$\{$BC$\}\_\{1\}\backslash )$

$\backslash (\backslash$mathrm$\{$BC$\}\_\{2\}\backslash )$

Given the price$-$quantity combinations from the preceding table, use the blue line $($circle symbol$)$ to plot Susan's demand for danishes on the following graph.

Hint: Assume that Susan's demand for danishes is a straight line. You should derive two points on the demand curve from the preceding graph. Then place the blue line on the following graph so that it passes through these two points.

Demand