Please solve for a-f according to the two images below. I will leave a good review!

Labor Supply. In the static (ie., one-period) consumption-labor framework of Chapter 2. suppose that the utility function of any given consumer is "(cn) = 1-0 in which c denotes consumption and n denotes labor. The terms o (the Greek lowercase letter "sigma"), w (the Greek lowercase letter "psi"), and O (the Greek lowercase letter "theta") are all exogenous parameter values and thus are taken as given by the consumer. The range of numerical values of these three exogenous parameters are o > 0, w > 0, and 9> 0. In the following analysis, the parameters w and O are always held fixed at their (though unspecified) respective positive numerical values. There are two different types of consumers. All consumers have identical budget constraints C=W .H and identical Lagrange functions -1 1- + 2.[w.n-c]. The only difference between the two categories of consumers is that the Type I consumer has a utility parameter o that is in the range 0 1.a. Based on the Lagrange function above, provide the first-order condition for c. Clearly display the first-order condition by drawing a box around it. b. Based on the Lagrange function above, provide the first-order condition for n. Clearly display the first-order condition by drawing a box around it. c. Using the first-order conditions computed in parts a and b, provide the important steps of algebra that lead to the consumption-labor optimality condition, which should be written as u (c,n) u (c,n) The term in ellipsis ("...") on the right-hand side is for you to determine. (Note: the final expression may not include the Lagrange multiplier.) d. If there are any c terms that appear in the consumption-labor optimality condition in part c, substitute them out using the budget constraint c= w-n. (Note: The final solution should not contain any c terms.) e. Suppose that the real wage has increased from w, to Wy . In the single figure below, provide a qualitative sketch that shows the changes in the consumption-labor optimality conditions for the two different types (Type I and Type II) of consumers for both the real wage w, and Wy. (Note: NO numerical analysis should be included in your solution; points may be deducted if the sketch relies on numeric examples.) f. Briefly (but carefully) justify the economic interpretation for the diagrammatic results in part e. (Note: "economic interpretation" is not simply a verbal restatement of the mathematics. ZERO points may be awarded if the economic interpretation/explanation is unclear.) consumption leisure