3) Derive Manuel's optimal bundle x₁*, X2* asa function of his income (mm) and p₁ (show yourwork).4) Suppose the market has a total of 20consumers. Ten consumers are identical toKarol, and ten are identical to Manuel.Find the market demand curve for kombucha asa function of mk, mm, and p1.If mkmM = 100, and p₁=2, what is the totalamount of kombucha that the consumersdemand? Two friends, Karol and Manuel, like to drinkkombucha (x₁) and matcha (x₂). Both X₁ and X2are expressed in ounces.The following utility function represents Karol'spreferences:1 122u (x1, x2) = x1 x3The following utility function representsManuel's preferences:u (x₁, x2) = √√x1 + x2Karol's income in dollars is denoted by mk, andManuel's income is denoted by mm. Both facethe same prices in the market, denoted by p₁and p2, for kombucha and matcha, respectively.Both prices are expressed in dollars per ounce.Assume p₂=1 throughout the whole question.1) Draw Karol's and Manuel's indifferencecurves in separate graphs and describe anyimportant similarities or differences betweenthe two.

An ‘optimal bundle’ is defined as a combination of two goods for a consumer that maximizes the…

3) Derive Manuel's optimal bundle x1*, X2* as a function of his income (mm) and p₁ (show your work). 4) Suppose the market has a total of 20 consumers. Ten consumers are identical to Karol, and ten are identical to Manuel. Find the market demand curve for kombucha as a function of mk, mm, and p1. If mk = mM = 100, and p₁=2, what is the total amount of kombucha that the consumers demand?