4. Say a consumer has W in initial wealth to invest. This wealth can be allocated between two assets: a safe asset that yields a gross return of 1 for every dollar invested, and a risky asset that yields a gross return of R per dollar invested. Assume that the consumer is an expected utility maximizer with a concave Bernoulli utility function defined over terminal wealth u(W). Denote by A the amount invested in the risky asset (therefore W - A is invested in the safe asset). The consumer chooses A so as to maximize the expected utility of terminal wealth, Elu(W)], where E is the expectations operator. (a) Write down the consumer's maximization problem and determine the first-order condition and the second-order condition. (b) We want to determine how the consumer's initial wealth W affects his choice of how much to invest in the risky asset, A. Implic- itly differentiate the first-order condition to determine an expres- sion for dA/dW. Use the second-order condition to determine if dA/dW >= < 0