20 H i} According to his 1945 AER article, what does Hayek view as the main problem facing an economy?II ii) How does Hayek argue that problem is solved in a free market economy? iii) Demonstrate how Hayek's solution works in the context of an economy with utility maximizing consumers and prot maximizing rms. That is, state the main efciency condition in an production economy and show how it is met in a free market. 3|] III Consider an exchange economy with two people, A and B, and two goods, X and Y. Person A has preferences, UA = 317.4 + 231% (1) where 3,, is person A's amount of good X and 3.5.1 is her amount of good Y. Similarly, person B has preferences, Us = rays (2) Finally, assume that person A's endowment is 5 units of X and 6 units of Y. Person B's endowment is 5 units of X and 4 units of Y. i) Draw an Edgeworth Box representing this economy, include the endowment point and indi'erence curves for each person {these curves don't have to he the exact repre- sentation of the preferences but do have to have the right shapes). ii) Find and draw the contract curve. iii) Draw the core for this economy and nd the end points that dene it. iv) Now con- sider a different endowment point at which A has 1 unit ofX and 0 units of Y and person