the question is complete

a) A nation's Gross Domestic Product (GDP) is a function of residual technology A, capital K, labor L, and natural resources N. A social planner will choose capital, labor, and resources in order to maximize GDP and therefore will solve the problem max GDP(K, L, N) = AKOLBNY K,L,N taking technology as given. Write down the first order conditions of the social planner's problem; that is, find the partial derivatives GDP GDP GDP set each equal to zero. OK " ON and b) A consumer receives utility u(21, 12) from consuming two goods r1, 12. The consumer always prefers more of these goods, but she is constrained by her budget piri + p212 = m. Therefore, she solves the problem max u(T1, "2) = $1 2 x1,12 1/2x3/4 subject to pili + P212 = m where p1, p2 are the prices of 21, 12 respectively and m is her income. i. Set up the maximization problem using the substitution method (that is, solve the budget constraint for one of the variables and substitute that expression into the utility function). Write down the first order condition for this problem. ii. Set up the maximization problem using a Lagrange multiplier (see section 14.1). Write down the first order conditions for this