(20 points) Using the performance-based online advertising pricing model introduced in the lecture. The optimal contract is given by tp=m[ra+rpra+ra+rprp1+p2(ra+rp)pp+p2ccc2pp1]tc=m[ra+rprppc+cpppcc+pc(ra+rp)cc1] Where m is impression, tp and tc payment per purchase and payment per clickthrough, ra and rp is risk of advertiser and risk of publisher, c and p piece rate per clickthrough and piece rate per purchase, and cc and pp is standard deviation of clickthrough and purchase error. a. Find the sign of dradtp and drpdtp. How do risk aversion parameters affect the optimal per-purchase payment? b. Find the sign of dradtc and drpdtc. How do risk aversion parameters affect the optimal per-clickthrough payment? (20 points) Using the performance-based online advertising pricing model introduced in the lecture. The optimal contract is given by tp=m[ra+rpra+ra+rprp1+p2(ra+rp)pp+p2ccc2pp1]tc=m[ra+rprppc+cpppcc+pc(ra+rp)cc1] Where m is impression, tp and tc payment per purchase and payment per clickthrough, ra and rp is risk of advertiser and risk of publisher, c and p piece rate per clickthrough and piece rate per purchase, and cc and pp is standard deviation of clickthrough and purchase error. a. Find the sign of dradtp and drpdtp. How do risk aversion parameters affect the optimal per-purchase payment? b. Find the sign of dradtc and drpdtc. How do risk aversion parameters affect the optimal per-clickthrough payment