The economy is populated with L farmers, that are consumers and producers at the sametime.As consumers they buy x and y from the market for consumption. Their utility function isu(x, y) = xy.As producers all farmers are endowed with one unit of labor that they can use to grow cropsand sell them on the market to earn income. All farmers have access to two productiontechnologiesQx(l) = ?xl and Qy(l) = ?yland they can choose between them (l is the amount of labor devoted to a specific technology,Qx is the amount of x produced and Qy is the amount of y produced).Let us denote Lx the number of people who chose to produce x and Ly the number of peoplewho chose to produce y.(a) (1 point) Write down individual earnings of a person who produces x and a personwho produces y (these should be algebraic expressions involving px, py, ?x, ?y)(b) (3 points)In equilibrium both x and y are demanded, so both x and y should besupplied. Producers can choose what to produce, so we want them to choose both (wewant some of them to choose to produce x and others to choose to produce y).Explain why it can not happen unless ?xpx = ?ypy. (Hint: what would happen if?xpx > ?ypy?, what would happen if ?xpx < ?ypy?)(c) (1 point) Let I be the equilibrium GDP in this economy. Write down the expressionsfor the demand for x and y and the supply of x and y (these should be algebraicexpressions involving I, px, py?x, ?y, Lx, Ly).(d) (1 point)Write down the expressions for I (this should be an algebraic expressioninvolving ?x, ?y, px, py, Lx, Ly)
The economy is populated with L farmers, that are consumers and producers at the same time. As consumers they buy x and y from the market for…
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