UCIMCAFFEINATED produces coffee according to the following tech nology: q = 200l1/2, where q denotes the quantity of coffee (in cups) produced and l...

Please help me solve no2 and no3 these two problems as soon as possible. Thank you!

2. UCIM—CAFFEINATED produces coffee according to the following tech—nology: q = 200l1/2, where q denotes the quantity of coffee (in cups)produced and l denotes the quantity of labor (hours) employed. In eachof the two following scenarios, calculate the firm’s profit—maximizinglevel of employment, I and output, (1, as well as the firm’s profits, 7r.Round to two decimal places. [40 points; 20 each] (a) UCIM—CAFFEINATED is a price taker in both the product market,with p = $3 per cup, and in the labor market, with the hourlywage rate given by w = $15. (b) While a price taker in the product market with p = $3 per cupof coffee, UCIM—CAFFEINATED is the sole demander of labor—i.e., a mon0psonist. Assume that the inverse supply of the labor is10(1) 2 83—0l' How do these solutions compare with those in part (a)? Econ 1053: final exam 2 3. Consider a small community of 10 identical individuals who consume aprivate consumption good (x) and a public good (z)—namely, securityor protection. Each individual’s preferences are defined over the twogoods as follows: U,- = 6:0, + 3J2 The cost of producing z is cz(z) =400 + 2 while the cost of producing a: is cm(x) : 100 + 4x. [40 points;20 each] (a) What would be the efficient provision of the public good in thiscommunity? (b) Find the market allocation guided by competitive equilibriumprices and identify the inefficiency of the “invisible hand.”