10. Consider the labour/leisure choice problem where the utility function is: U(c,l) = c²l where c is consumption of goods and services, and l is leisure time. The constraint is: w(T – 1) + N = c, where w is the real wage, T is time available for work and leisure and N is income derived from non-labour sources (rents, profits etc). This is all spent on consumption c. (a) Form the Lagrangean, find optimal consumption (c*) and leisure (1*) in terms of w, and N. Do not check the second order conditions. (b) Labour time advanced (L*) is T– l*. Define this in terms of w,T and N. (c) Show that optimal L* change positively as the real wage (w) increases.

workers ouput marginal product  total cost average total cost marginal cost 0 0 0 200 0 $0 1 20 20 300 $15 $5 2 50 30 400 $8 $3.33 3 90 40 500 $5.56 $2.50 4 120 30 600 $5 $3.33 5 140 20 700 $5 $5 6 150 10 800 $5.33 $10 7 155 5 900 $5.8 $20 can you explain diminishing marginal product based on these numbers?

Please see attachment and table given in it .n solve part b asap within 40min. Will give you multiple upvotes only for the correct answer. Thank you